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Part VIII.

Panel and Pooled Data
Panel and pool data involve observations that possess both cross-section, and within-crosssection identifiers. Generally speaking, we distinguish between the two by noting that pooled time-series, cross-section data refer to data with relatively few cross-sections, where variables are held in cross-section specific individual series, while panel data correspond to data with large numbers of cross-sections, with variables held in single series in stacked form. The discussion of these data is divided into parts. Pooled data structures are discussed first: • Chapter 35. “Pooled Time Series, Cross-Section Data,” on page 565 outlines tools for working with pooled time series, cross-section data, and estimating standard equation specifications which account for the pooled structure of the data. Stacked panel data are described separately: • In Chapter 9. “Advanced Workfiles,” beginning on page 213 of User’s Guide I, we describe the basics of structuring a workfile for use with panel data. Once a workfile is structured as a panel workfile, EViews provides you with different tools for working with data in the workfile, and for estimating equation specifications using both the data and the panel structure. • Chapter 36. “Working with Panel Data,” beginning on page 615, outlines the basics of working with panel workfiles. • Chapter 37. “Panel Estimation,” beginning on page 647 describes estimation in panel structured workfiles.

564—Part VIII. Panel and Pooled Data

Chapter 35. Pooled Time Series, Cross-Section Data
Data often contain information on a relatively small number of cross-sectional units observed over time. For example, you may have time series data on GDP for a number of European nations. Or perhaps you have state level data on unemployment observed over time. We term such data pooled time series, cross-section data. EViews provides a number of specialized tools to help you work with pooled data. EViews will help you manage your data, perform operations in either the time series or the crosssection dimension, and apply estimation methods that account for the pooled structure of your data. The EViews object that manages time series/cross-section data is called a pool. The remainder of this chapter will describe how to set up your data to work with pools, and how to define and work with pool objects. Note that the data structures described in this chapter should be distinguished from data where there are large numbers of cross-sectional units. This type of data is typically termed panel data. Working with panel structured data in EViews is described in Chapter 36. “Working with Panel Data,” on page 615 and Chapter 37. “Panel Estimation,” beginning on page 647.

The Pool Workfile
The first step in working with pooled data is to set up a pool workfile. There are several characteristics of an EViews workfile that allow it to be used with pooled time series, crosssection data. First, a pool workfile is an ordinary EViews workfile structured to match the time series dimension of your data. The range of your workfile should represent the earliest and latest dates or observations you wish to consider for any of the cross-section units. For example, if you want to work with data for some firms from 1932 to 1954, and data for other firms from 1930 to 1950, you should create a workfile ranging from 1930 to 1954. Second, the pool workfile should contain EViews series that follow a user-defined naming convention. For each cross-section spe-

566—Chapter 35. Pooled Time Series, Cross-Section Data

cific variable, you should have a separate series corresponding to each cross-section/ variable combination. For example, if you have time series data for an economic variable like investment that differs for each of 10 firms, you should have 10 separate investment series in the workfile with names that follow the user-defined convention. Lastly, and most importantly, a pool workfile must contain one or more pool objects, each of which contains a (possibly different) description of the pooled structure of your workfile in the form of rules specifying the user-defined naming convention for your series. There are various approaches that you may use to set up your pool workfile: • First, you may simply create a new workfile in the usual manner, by describing, the time series structure of your data. Once you have a workfile with the desired structure, you may define a pool object, and use this object as a tool in creating the series of interest and importing data into the series. • Second, you may create an EViews workfile containing your data in stacked form. Once you have your stacked data, you may use the built-in workfile reshaping tools to create a workfile containing the desired structure and series. Both of these procedures require a bit more background on the nature of the pool object, and the way that your pooled data are held in the workfile. We begin with a brief description of the basic components of the pool object, and then return to a description of the task of setting up your workfile and data (“Setting up a Pool Workfile” on page 571).

The Pool Object
Before describing the pooled workfile in greater detail, we must first provide a brief description of the EViews pool object. We begin by noting that the pool object serves two distinct roles. First, the pool contains a set of definitions that describe the structure of the pooled time series, cross-section data in your workfile. In this role, the pool object serves as a tool for managing and working with pooled data, much like the group object serves is used as a tool for working with sets of series. Second, the pool provides procedures for estimating econometric models using pooled data, and examining and working with the results from this estimation. In this role, the pool object is analogous to an equation object that is used to estimate econometric specifications. In this section, we focus on the definitions that serve as the foundation for the pool object and simple tools for managing your pool object. The tools for working with data are described in “Working with Pooled Data,” beginning on page 578, and the role of the pool object in estimation is the focus of “Pooled Estimation,” beginning on page 586.

The Pool Object—567

Defining a Pool Object
There are two parts to the definitions in a pool object: the cross-section identifiers, and optionally, definitions of groups of identifiers.

Cross-section Identifiers
The central feature of a pool object is a list of cross-section members which provides a naming convention for series in the workfile. The entries in this list are termed cross-section identifiers. For example, in a cross-country study, you might use “_USA” to refer to the United States, “_KOR” to identify Korea, “_JPN” for Japan, and “_UK” for the United Kingdom. Since the cross-section identifiers will be used as a base in forming series names, we recommend that they be kept relatively short. Specifying the list cross-section identifiers in a pool tells EViews about the structure of your data. When using a pool with the four cross-section identifiers given above, you instruct EViews to work with separate time series data for each of the four countries, and that the data may be held in series that contain the identifiers as part of the series names. The most direct way of creating a pool object is to select Object/New Object.../Pool. EViews will open the pool specification view into which you should enter or copy-and-paste a list of identifiers, with individual entries separated by spaces, tabs, or carriage returns. Here, we have entered four identifiers on separate lines. There are no special restrictions on the labels that you can use for cross-section identifiers, though you must be able to form legal EViews series names containing these identifiers. Note that we have used the “_” character at the start of each of the identifiers in our list; this is not necessary, but you may find that it makes it easier to spot the identifier when it is used as the end of a series name. Before moving on, it is important to note that a pool object is simply a description of the underlying structure of your data, so that it does not itself contain series or data. This separation of the object and the data has important consequences. First, you may use pool objects to define multiple sets of cross-section identifiers. Suppose, for example, that the pool object POOL01 contains the definitions given above. You may also have a POOL02 that contains the identifiers “_GER,” “_AUS,” “_SWTZ,” and a POOL03 that contains the identifiers “_JPN” and “_KOR”. Each of these three pool objects defines a

568—Chapter 35. Pooled Time Series, Cross-Section Data

different set of identifiers, and may be used to work with different sets of series in the workfile. Alternatively, you may have multiple pool objects in a workfile, each of which contain the same list of identifiers. A POOL04 that contains the same identifiers as POOL01 may be used to work with data from the same set of countries. Second, since pool objects contain only definitions and not series data, deleting a pool will not delete underlying series data. You may, however, use a pool object to delete, create, and manipulate underlying series data.

Group Definitions
In addition to the main list of cross-section identifiers, you may define groups made up of subsets of your identifiers. To define a group of identifiers, you should enter the keyword “@GROUP” followed by a name for the group, and the subset of the pool identifiers that are to be used in the group. EViews will define a group using the specified name and any identifiers provided. We may, for example, define the ASIA group containing the “_JPN” and “_KOR” identifiers, or the NORTHAMERICA group containing the “_USA” identifier by adding:
@group asia _jpn _kor @group northamerica _usa

to the pool definition. These subsets of cross-section identifiers may be used to define virtual series indicating whether a given observation corresponds to a given subgroup or not. The ASIA group, for example, can be used along with special tools to identify whether a given observation should be viewed as coming from Japan or Korea, or from one of the other countries in the pool. We describe this functionality in greater detail in “Pool Series” on page 570.

Viewing or Editing Definitions
You may, at any time, change the view of an existing pool object to examine the current list of cross-section identifiers and group definitions. Simply push the Define button on the toolbar, or select View/Cross-Section Identifiers. If desired, you can edit the list of identifiers or group definitions.

Copying a Pool Object
Typically, you will work with more than one pool object. Multiple pools are used to define various subsamples of cross-section identifiers, or to work with different pooled estimation specifications. To copy a pool object, open the original pool, and select Object/Copy Object… Alternatively, you can highlight the name of the pool in the workfile window, and either select

Pooled Data—569

Object/Copy Selected… in the main workfile toolbar, or right mouse-click and select Object/Copy... and enter the new name

Pooled Data
As noted previously, all of your pooled data will be held in ordinary EViews series. These series can be used in all of the usual ways: they may, among other things, be tabulated, graphed, used to generate new series, or used in estimation. You may also use a pool object to work with sets of the individual series. There are two classes of series in a pooled workfile: ordinary series and cross-section specific series.

Ordinary Series
An ordinary series is one that has common values across all cross-sections. A single series may be used to hold the data for each variable, and these data may be applied to every cross-section. For example, in a pooled workfile with firm cross-section identifiers, data on overall economic conditions such as GDP or money supply do not vary across firms. You need only create a single series to hold the GDP data, and a single series to hold the money supply variable. Since ordinary series do not interact with cross-sections, they may be defined without reference to a pool object. Most importantly, there are no naming conventions associated with ordinary series beyond those for ordinary EViews objects.

Cross-section Specific Series
Cross-section specific series are those that have values that differ between cross-sections. A set of these series are required to hold the data for a given variable, with each series corresponding to data for a specific cross-section. Since cross-section specific series interact with cross-sections, they should be defined in conjunction with the identifiers in pool objects. Suppose, for example, that you have a pool object that contains the identifiers “_USA,” “_KOR,” “_JPN,” and “_UK”, and that you have time series data on GDP for each of the cross-section units. In this setting, you should have a four cross-section specific GDP series in your workfile. The key to naming your cross-section specific series is to use names that are a combination of a base name and a cross-section identifier. The cross-section identifiers may be embedded at an arbitrary location in the series name, so long as this is done consistently across identifiers. You may elect to place the identifier at the end of the base name, in which case, you should name your series “GDP_USA,” “GDP_KOR,” “GDP_JPN,” and “GDP_UK”. Alternatively, you may choose to put the section identifiers in front of the name, so that you have the

570—Chapter 35. Pooled Time Series, Cross-Section Data

names “_USAGDP,” “_KORGDP,” “_JPNGDP,” and “_UKGDP”. The identifiers may also be placed in the middle of series names—for example, using the names “GDP_USAINF,” “GDP_KORIN,” “GDP_JPNIN,” “GDP_UKIN”. It really doesn’t matter whether the identifiers are used at the beginning, middle, or end of your cross-section specific names; you should adopt a naming style that you find easiest to manage. Consistency in the naming of the set of cross-section series is, however, absolutely essential. You should not, for example, name your four GDP series “GDP_USA”, “GDP_KOR”, “_JPNGDPIN”, “_UKGDP”, as this will make it impossible for EViews to refer to the set of series using a pool object.

Pool Series
Once your series names have been chosen to correspond with the identifiers in your pool, the pool object can be used to work with a set of series as though it were a single item. The key to this processing is the concept of a pool series. A pool series is actually a set of series defined by a base name and the entire list of crosssection identifiers in a specified pool. Pool series are specified using the base name, and a “?” character placeholder for the cross-section identifier. If your series are named “GDP_USA”, “GDP_KOR”, “GDP_JPN”, and “GDP_UK”, the corresponding pool series may be referred to as “GDP?”. If the names of your series are “_USAGDP”, “_KORGDP”, “_JPNGDP”, and “_UKGDP”, the pool series is “?GDP”. When you use a pool series name, EViews understands that you wish to work with all of the series in the workfile that match the pool series specification. EViews loops through the list of cross-section identifiers in the specified pool, and substitutes each identifier in place of the “?”. EViews then uses the complete set of cross-section specific series formed in this fashion. In addition to pool series defined with “?”, EViews provides a special function, @INGRP, that you may use to generate a group identity pool series that takes the value 1 if an observation is in the specified group, and 0 otherwise. Consider, for example, the @GROUP for “ASIA” defined using the identifiers “_KOR” and “_JPN”, and suppose that we wish to create a dummy variable series for whether an observation is in the group. One approach to representing these data is to create the following four cross-section specific series:
series asia_usa = 0 series asia_kor = 1 series asia_jpn = 1 series asia_uk = 0

Setting up a Pool Workfile—571

and to refer to them collectively as the pool series “ASIA_?”. While not particularly difficult to do, this direct approach becomes more cumbersome the greater the number of cross-section identifiers. More easily, we may use the special pool series expression:
@ingrp(asia)

to define a special virtual pool series in which each observation takes a 0 or 1 indicator for whether an observation is in the specified group. This expression is equivalent to creating the four cross-section specific series, and referring to them as “ASIA_?”. We must emphasize that pool series specifiers using the “?” and the @INGRP function may only be used through a pool object, since they have no meaning without a list of cross-section identifiers. If you attempt to use a pool series outside the context of a pool object, EViews will attempt to interpret the “?” as a wildcard character (see Appendix A. “Wildcards,” on page 559 in the Command and Programming Reference). The result, most often, will be an error message saying that your variable is not defined.

Setting up a Pool Workfile
Your goal in setting up a pool workfile is to obtain a workfile containing individual series for ordinary variables, sets of appropriately named series for the cross-section specific data, and pool objects containing the related sets of identifiers. The workfile should have frequency and range matching the time series dimension of your pooled data. There are two basic approaches to setting up such a workfile. The direct approach involves first creating an empty workfile with the desired structure, and then importing data into individual series using either standard or pool specific import methods. The indirect approach involves first creating a stacked representation of the data in EViews, and then using EViews built-in reshaping tools to set up a pooled workfile.

Direct Setup
The direct approach to setting up your pool workfile involves three distinct steps: first creating a workfile with the desired time series structure; next, creating one or more pool objects containing the desired cross-section identifiers; and lastly, using pool object tools to import data into individual series in the workfile.

Creating the Workfile and Pool Object
The first step in the direct setup is to create an ordinary EViews workfile structured to match the time series dimension of your data. The range of your workfile should represent the earliest and latest dates or observations you wish to consider for any of the cross-section units.

572—Chapter 35. Pooled Time Series, Cross-Section Data

Simply select File/New workfile... to bring up the Workfile Create dialog which you will use to describe the structure of your workfile. For additional detail, see “Creating a Workfile by Describing its Structure” on page 35 of User’s Guide I. For example, to create a pool workfile that has annual data ranging from 1950 to 1992, simply select Annual in the Frequency combo box, and enter “1950” as the Start date and “1992” as the End date. Next, you should create one or more pool objects containing cross-section identifiers and group definitions as described in “The Pool Object” on page 566.

Importing Pooled Data
Lastly, you should use one of the various methods for importing data into series in the workfile. Before considering the various approaches, we require an understanding the various representations of pooled time series, cross-section data that you may encounter. Bear in mind that in a pooled setting, a given observation on a variable may be indexed along three dimensions: the variable, the cross-section, and the time period. For example, you may be interested in the value of GDP, for the U.K., in 1989. Despite the fact that there are three dimensions of interest, you will eventually find yourself working with a two-dimensional representation of your pooled data. There is obviously no unique way to organize three-dimensional data in two-dimensions, but several formats are commonly employed.

Here, the base name “C” represents consumption, while “G” represents government expenditure. Each country has its own separately identified column for consumption, and its own column for government expenditure. EViews pooled workfiles are structured to work naturally with data that are unstacked, since the sets of cross-section specific series in the pool workfile correspond directly to the

Setting up a Pool Workfile—573

multiple columns of unstacked source data. You may read unstacked data directly into EViews using the standard workfile creation procedures described in “Creating a Workfile by Reading from a Foreign Data Source” on page 39 of User’s Guide I. Each cross-section specific variable should be read as an individual series, with the names of the resulting series follow the pool naming conventions given in your pool object. Ordinary series may be imported in the usual fashion with no additional complications. In this example, we should use the standard EViews tools to read separate series for each column. We create the individual series “YEAR”, “C_USA”, “C_KOR”, “C_JPN”, “G_USA”, “G_JPN”, and “G_KOR”.

Stacked Data
Pooled data can also be arranged in stacked form, where all of the data for a variable are grouped together in a single column. In the most common form, the data for different cross-sections are stacked on top of one another, with all of the sequentially dated observations for a given cross-section grouped together. We may say that these data are stacked by cross-section:
id _usa _usa _usa _usa year 1954 c 61.6 g 17.8

… …
1992

… …
68.1

… …
13.2

…
_kor _kor _kor

…
1954

…
77.4

…
17.6

…
1992

…
na

…
na

Alternatively, we may have data that are stacked by date, with all of the observations of a given period grouped together:

574—Chapter 35. Pooled Time Series, Cross-Section Data

per 1954 1954 1954 1954

id _usa _uk _jpn _kor

c 61.6 62.4 66 77.4

g 17.8 23.8 18.7 17.6

…
1992 1992 1992 1992

…
_usa _uk _jpn _kor

…
68.1 67.9 54.2 na

…
13.2 17.3 7.6 na

Each column again represents a single variable, but within each column, all of the cross-sections for a given year are grouped together. If data are stacked by year, you should make certain that the ordering of the cross-sectional identifiers within a year is consistent across years. There are to primary approaches to importing data into your pool series: you may read the data in stacked form then use EViews tools to restructure the data in pool form, or you may directly read or copy the data into a stacked representation of the pooled series. Indirect Setup (Restructuring) of Stacked Data The easiest approach to reading stacked pool data is to create an EViews workfile containing the data in stacked form, and then use the built-in workfile reshaping tools to create a pool workfile with the desired structure and data. (Alternately, you can perform the first step and simply work with the data in stacked form: see Chapter 36. “Working with Panel Data,” on page 615 for details.) The first step in the indirect setup of a pool workfile is to create a workfile containing the contents of your stacked data file. You may manually create the workfile and import the stacked series data, or you may use EViews tools for opening foreign source data directly into a new workfile (“Creating a Workfile by Reading from a Foreign Data Source” on page 39 of User’s Guide I). Once you have your stacked data in an EViews workfile, you may use the workfile reshaping tools to unstack the data into a pool workfile page. In addition to unstacking the data into multiple series, EViews will create a pool object containing identifiers obtained from patterns in the series names. See “Reshaping a Workfile,” beginning on page 248 of User’s Guide I for a general discussion of reshaping, and “Unstacking a Workfile” on page 251 of User’s Guide I for a more specific discussion of the unstack procedure.

Setting up a Pool Workfile—575

The indirect method is generally easier to use than the direct approach and has the advantage of not requiring that the stacked data be balanced. It has the disadvantage of using more computer memory since EViews must have two copies of the source data in memory at the same time. Direct Import of Stacked Data An alternative approach is to enter or read the data directly into the workfile using a pool object. You may enter or copy-and-paste data from the source into and a stacked representation of your data, or you may use the pool object to describe how to read the stacked data into the unstacked workfile. To enter data or copy-and-paste, you use the pool object to create a stacked representation of the data in EViews: • First, specify which time series observations will be included in your stacked spreadsheet by setting the workfile sample. • Next, open the pool, then select View/Spreadsheet View… EViews will prompt you for a list of series. You can enter ordinary series names or pool series names. If the series exist, then EViews will display the data in the series. If the series do not exist, then EViews will create the series or group of series, using the cross-section identifiers if you specify a pool series. • EViews will open the stacked spreadsheet view of the pool series. If desired, click on the Order +/– button to toggle between stacking by cross-section and stacking by date. • Click Edit +/– to turn on edit mode in the spreadsheet window, and enter your data, or cut-and-paste from another application. For example, if we have a pool object that contains the identifiers “_USA”, “_UK”, “_JPN”, and “_KOR”, we can instruct EViews to create the series C_USA, C_UK, C_JPN, C_KOR, and G_USA, G_UK, G_JPN, G_KOR, and YEAR simply by entering the pool series names “C?”, “G?” and the ordinary series name “YEAR”, and pressing OK. EViews will open a stacked spreadsheet view of the series in your list. Here we see the series stacked by cross-section, with the pool or ordinary series names in the column header, and the cross-section/date identifiers labeling each row. Note that since YEAR is an ordinary series, its values are repeated for each cross-section in the stacked spreadsheet.

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If desired, click on Order +/– to toggle between stacking methods to match the organization of the data to be imported. Click on Edit +/– to turn on edit mode, and enter or cutand-paste into the window. Alternatively, you can import stacked data from a file using import tools built into the pool object. While the data in the file may be stacked either by cross-section or by period, EViews does require that the stacked data are “balanced,” and that the cross-sections ordering in the file matches the cross-sectional identifiers in the pool. By “balanced,” we mean that if the data are stacked by cross-section, each cross-section should contain exactly the same number of periods—if the data are stacked by date, each date should have exactly the same number of cross-sectional observations arranged in the same order. We emphasize that only the representation of the data in the import file needs to be balanced; the underlying data need not be balanced. Notably, if you have missing values for some observations, you should make certain that there are lines in the file representing the missing values. In the two examples above, the underlying data are not balanced, since information is not available for Korea in 1992. The data in the file have been balanced by including an observation for the missing data. To import stacked pool data from a file, first open the pool object, then select Proc/Import Pool data (ASCII, .XLS, .WK?)…It is important that you use the import procedure associated with the pool object, and not the standard file import procedure. Select your input file in the usual fashion. If you select a spreadsheet file, EViews will open a spreadsheet import dialog prompting you for additional input.

Setting up a Pool Workfile—577

Much of this dialog should be familiar from the discussion in “Importing Data from a Spreadsheet or Text File” on page 105 of User’s Guide I. First, indicate whether the pool series are in rows or in columns, and whether the data are stacked by crosssection, or stacked by date. Next, in the pool series edit box, enter the names of the series you wish to import. This list may contain any combination of ordinary series names and pool series names. Lastly, fill in the sample information, starting cell location, and optionally, the sheet name. When you specify your series using pool series names, EViews will, if necessary, create and name the corresponding set of pool series using the list of cross-section identifiers in the pool object. If you list an ordinary series name, EViews will, if needed, create a single series to hold the data. EViews will read the contents of your file into the specified pool variables using the sample information. When reading into pool series, the first set of observations in the file will be placed in the individual series corresponding to the first cross-section (if reading data that is grouped by cross-section), or the first sample observation of each series in the set of crosssectional series (if reading data that is grouped by date), and so forth. If you read data into an ordinary series, EViews will continually assign values into the corresponding observation of the single series, so that upon completion of the import procedure, the series will contain the last set of values read from the file. The basic technique for importing stacked data from ASCII text files is analogous, but the corresponding dialog contains many additional options to handle the complexity of text files.

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For a discussion of the text specific settings in the dialog, see “Importing ASCII Text Files” on page 122 of User’s Guide I.

Working with Pooled Data
The underlying series for each cross-section member are ordinary series, so all of the EViews tools for working with the individual cross-section series are available. In addition, EViews provides you with a number of specialized tools which allow you to work with your pool data. Using EViews, you can perform, in a single step, similar operations on all the series corresponding to a particular pooled variable.

Generating Pooled Data
You can generate or modify pool series using the pool series genr procedure. Click on PoolGenr on the pool toolbar and enter a formula as you would for a regular genr, using pool series names as appropriate. Using our example from above, entering:
ratio? = g?/g_usa

Generation of a pool series applies the formula you supply using an implicit loop across cross-section identifiers, creating or modifying one or more series as appropriate.

Working with Pooled Data—579

You may use pool and ordinary genr together to generate new pool variables. For example, to create a dummy variable that is equal to 1 for the US and 0 for all other countries, first select PoolGenr and enter:
dum? = 0

to initialize all four of the dummy variable series to 0. Then, to set the US values to 1, select Quick/Generate Series… from the main menu, and enter:
dum_usa = 1

It is worth pointing out that a superior method of creating this pool series is to use @GROUP to define a group called US containing only the “_USA” identifier (see “Group Definitions” on page 568), then to use the @INGRP function:
dum? = @ingrp(us)

to generate and implicitly refer to the four series (see “Pool Series” on page 570). To modify a set of series using a pool, select PoolGenr, and enter the new pool series expression:
dum? = dum? * (g? > c?)

It is worth the reminder that the method used by the pool genr is to perform an implicit loop across the cross-section identifiers. This implicit loop may be exploited in various ways, for example, to perform calculations across cross-sectional units in a given period. Suppose, we have an ordinary series SUM which is initialized to zero. The pool genr expression:
sum = sum + c?

Bear in mind that this example is provided merely to illustrate the notion of implicit looping, since EViews provides built-in features to compute period-specific statistics.

Examining Your Data
Pool workfiles provide you with the flexibility to examine cross-section specific series as individual time series or as part of a larger set of series.

Examining Unstacked Data
Simply open an individual series and work with it using the standard tools available for examining a series object. Or create a group of series and work with the tools for a group

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object. One convenient way to create groups of series is to use tools for creating groups out of pool and ordinary series; another is to use wildcards expressions in forming the group.

Examining Stacked Data
As demonstrated in “Stacked Data,” beginning on page 573, you may use your pool object to view your data in stacked spreadsheet form. Select View/Spreadsheet View…, and list the series you wish to display. The names can include both ordinary and pool series names. Click on the Order +/– button to toggle between stacking your observations by cross-section and by date. We emphasize that stacking your data only provides an alternative view of the data, and does not change the structure of the individual series in your workfile. Stacking data is not necessary for any of the data management or estimation procedures described below.

Calculating Descriptive Statistics
EViews provides convenient built-in features for computing various descriptive statistics for pool series using a pool object. To display the Pool Descriptive Statistics dialog, select View/Descriptive Statistics… from the pool toolbar. In the edit box, you should list the ordinary and pooled series for which you want to compute the descriptive statistics. EViews will compute the mean, median, minimum, maximum, standard deviation, skewness, kurtosis, and the Jarque-Bera statistic for these series. First, you should choose between the three sample options on the right of the dialog: • Individual: uses the maximum number of observations available. If an observation on a variable is available for a particular crosssection, it is used in computation. • Common: uses an observation only if data on the variable are available for all crosssections in the same period. This method is equivalent to performing listwise exclusion by variable, then cross-sectional casewise exclusion within each variable. • Balanced: includes observations when data on all variables in the list are available for all cross-sections in the same period. The balanced option performs casewise exclusion by both variable and cross-section. Next, you should choose the computational method corresponding to one of the four data structures:

Working with Pooled Data—581

• Stacked data: display statistics for each variable in the list, computed over all crosssections and periods. These are the descriptive statistics that you would get if you ignored the pooled nature of the data, stacked the data, and computed descriptive statistics. • Stacked – means removed: compute statistics for each variable in the list after removing the cross-sectional means, taken over all cross-sections and periods. • Cross-section specific: show the descriptive statistics for each cross-sectional variable, computed across all periods. These are the descriptive statistics derived by computing statistics for the individual series. • Time period specific: compute period-specific statistics. For each period, compute the statistic using data on the variable from all the cross-sectional units in the pool. Click on OK, and EViews will display a pool view containing tabular output with the requested statistics. If you select Stacked data or Stacked - means removed, the view will show a single column containing the descriptive statistics for each ordinary and pool series in the list, computed from the stacked data. If you select Cross-section specific, EViews will show a single column for each ordinary series, and multiple columns for each pool series. If you select Time period specific, the view will show a single column for each ordinary or pool series statistic, with each row of the column corresponding to a period in the workfile. Note that there will be a separate column for each statistic computed for an ordinary or pool series; a column for the mean, a column for the variance, etc. You should be aware that the latter two methods may produce a great deal of output. Crosssection specific computation generates a set of statistics for each pool series/cross-section combination. If you ask for statistics for three pool series and there are 20 cross-sections in your pool, EViews will display 60 columns of descriptive statistics. For time period specific computation, EViews computes a set of statistics for each date/series combination. If you have a sample with 100 periods and you provide a list of three pool series, EViews will compute and display a view with columns corresponding to 3 sets of statistics, each of which contains values for 100 periods. If you wish to compute period-specific statistics, you may save the results in series objects. See “Making Period Stats” on page 583.

Computing Unit Root Tests
EViews provides convenient tools for computing multiple-series unit root tests for pooled data using a pool object. You may use the pool to compute one or more of the following types of unit root tests: Levin, Lin and Chu (2002), Breitung (2000), Im, Pesaran and Shin (2003), Fisher-type tests using ADF and PP tests—Maddala and Wu (1999) and Choi (2001), and Hadri (2000). To compute the unit root test, select View/Unit Root Test…from the menu of a pool object.

582—Chapter 35. Pooled Time Series, Cross-Section Data

Enter the name of an ordinary or pool series in the topmost edit field, then specify the remaining settings in the dialog. These tests, along with the settings in the dialog, are described in considerable detail in “Panel Unit Root Test” on page 391.

Performing Cointegration Tests
Panel cointegration tests are available as a view of a group in a panel workfile or for a group of pooled series defined using a pool object. EViews allows you to conduct several different tests: Pedroni (1999, 2004), Kao (1999) and Fisher-type test using Johansen’s test methodology (Maddala and Wu, 1999). To compute the panel cointegration test for pooled data, select Views/Cointegration Test… from the menu of a pool object. Enter the names of at least two pool series or a combination of at least two pool and ordinary series in the topmost Variables field, then specify the rest of the options. The remaining options are identical to those encountered when performing panel cointegration testing using a group in a panel-structured workfile. For details, see “Panel Cointegration Testing,” beginning on page 698. In this example, specify two pool variables “IVM?” and “MM?” and one ordinary variable “X”, so that EViews tests for cointegration between the pool series IVM? against pool series MM? and the stacked common series X.

Working with Pooled Data—583

Making a Group of Pool Series
If you click on Proc/Make Group… and enter the names of ordinary and pool series. EViews will use the pool definitions to create an untitled group object containing the specified series. This procedure is useful when you wish to work with a set of pool series using the tools provided for groups. Suppose, for example, that you wish to compute the covariance matrix for the C? series. Simply open the Make Group dialog, and enter the pool series name “C?”. EViews will create a group containing the set of cross-section specific series, with names beginning with “C” and ending with a cross-section identifier. Then, in the new group object, you may select View/Covariance Analysis... to compute the covariance matrix of the series in the group. EViews will perform the analysis using all of the individual series in the group.

Making Period Stats
To save period-specific statistics in series in the workfile, select Proc/Make Period Stats Series… from the pool window, and fill out the dialog. In the edit window, list the series for which you wish to calculate period-statistics. Next, select the particular statistics you wish to compute, and choose a sample option. EViews will save your statistics in new series and will open an untitled group window to display the results. The series will be named automatically using the base name followed by the name of the statistic (MEAN, MED, VAR, SD, OBS, SKEW, KURT, JARQ, MAX, MIN). In this example, EViews will save the statistics using the names CMEAN, GMEAN, CVAR, GVAR, CMAX, GMAX, CMIN, and GMIN.

Making a System
Suppose that you wish to estimate a complex specification that cannot easily be estimated using the built-in features of the pool object. For example, you may wish to estimate a pooled equation imposing arbitrary coefficient restrictions, or using specialized GMM techniques that are not available in pooled estimation. In these circumstances, you may use the pool to create a system object using both common and cross-section specific coefficients, AR terms, and instruments. The resulting system

584—Chapter 35. Pooled Time Series, Cross-Section Data

object may then be further customized, and estimated using all of the techniques available for system estimation. Select Proc/Make System… and fill out the dialog. You may enter the dependent variable, common and crosssection specific variables, and use the checkbox to allow for cross-sectional fixed effects. You may also enter a list of common and cross-section specific instrumental variables, and instruct EViews to add lagged dependent and independent regressors as instruments in models with AR specifications. When you click on OK, EViews will take your specification and create a new system object containing a single equation for each cross-section, using the specification provided.

Deleting/Storing/Fetching Pool Data
Pools may be used to delete, store, or fetch sets of series. Simply select Proc/Delete pool series…, Proc/Store pool series (DB)…, or Proc/Fetch pool series (DB)… as appropriate, and enter the ordinary and pool series names of interest. If, for example, you instruct EViews to delete the pool series C?, EViews will loop through all of the cross-section identifiers and delete all series whose names begin with the letter “C” and end with the cross-section identifier.

Exporting Pooled Data
You can export your data into a disk file, or into a new workfile or workfile page, by reversing one of the procedures described above for data input.

Working with Pooled Data—585

To write pooled data in stacked form into an ASCII text, Excel, or Lotus worksheet file, first open the pool object, then from the pool menu, select Proc/Export Pool data (ASCII, .XLS, .WK?)…. Note that in order to access the pool specific export tools, you must select this procedure from the pool menu, not from the workfile menu. EViews will first open a file dialog prompting you to specify a file name and type. If you provide a new name, EViews will create the file; otherwise it will prompt you to overwrite the existing file. Once you have specified your file, a pool write dialog will be displayed. Here we see the Excel Spreadsheet Export dialog. Specify the format of your data, including whether to write series in columns or in rows, and whether to stack by cross-section or by period. Then list the ordinary series, groups, and pool series to be written to the file, the sample of observations to be written, and select any export options. When you click on OK, EViews will write the specified file. Since EViews allows you to both read and write data that are unstacked, stacked by crosssection, or stacked by date, you may use the pool import and export procedures to restructure your data in accordance with your needs. Alternatively, you may use the workfile reshaping tools to stack the pooled data in a new workfile page. From the main workfile menu, select Proc/Reshape Current Page/Stack in New Page... to open the Workfile Stack dialog, and enter the name of a pool object in the top edit field, and the names of the ordinary series, groups, and pool series to be stacked in the second edit field.

586—Chapter 35. Pooled Time Series, Cross-Section Data

The Order of obs option allows you to order the data in Stacked form (stacking the data by series, which orders by crosssection), or in Interleaved format (stacked the data by interleaving series, which orders the data by period or date). The default naming rule for series in the destination is to use the base name. For example, if you stack the pool series “SALES?” and the individual series GENDER, the corresponding stacked series will, by default, be named “SALES”, and “GENDER”. If use of the default naming convention will create problems in the destination workfile, you should use the Name for stacked series field to specify an alternative. If, for example, you enter “_NEW”, the target names will be formed by taking the base name, and appending the additional text, as in “SALES_NEW” and “GENDER_NEW”. See “Stacking a Workfile” on page 257 of User’s Guide I for a more detailed discussion of the workfile stacking procedure.

Pooled Estimation
EViews pool objects allow you to estimate your model using least squares or instrumental variables (two-stage least squares), with correction for fixed or random effects in both the cross-section and period dimensions, AR errors, GLS weighting, and robust standard errors, all without rearranging or reordering your data. We begin our discussion by walking you through the steps that you will take in estimating a pool equation. The wide range of models that EViews supports means that we cannot exhaustively describe all of the settings and specifications. A brief background discussion of the supported techniques is provided in “Estimation Background,” beginning on page 601.

Estimating a Pool Equation
To estimate a pool equation specification, simply press the Estimate button on your pool object toolbar or select Proc/Estimate... from the pool menu, and the basic pool estimation dialog will open:

Pooled Estimation—587

First, you should specify the estimation settings in the lower portion of the dialog. Using the Method combo box, you may choose between LS - Least Squares (and AR), ordinary least squares regression, TSLS - Two-Stage Least Squares (and AR), two-stage least squares (instrumental variable) regression. If you select the latter, the dialog will differ slightly from this example, with the provision of an additional tab (page) for you to specify your instruments (see “Instruments” on page 592). You should also provide an estimation sample in the Sample edit box. By default, EViews will use the specified sample string to form use the largest sample possible in each crosssection. An observation will be excluded if any of the explanatory or dependent variables for that cross-section are unavailable in that period. The checkbox for Balanced Sample instructs EViews to perform listwise exclusion over all cross-sections. EViews will eliminate an observation if data are unavailable for any cross-section in that period. This exclusion ensures that estimates for each cross-section will be based on a common set of dates. Note that if all of the observations for a cross-section unit are not available, that unit will temporarily be removed from the pool for purposes of estimation. The EViews output will inform you if any cross-section were dropped from the estimation sample. You may now proceed to fill out the remainder of the dialog.

Regressors and AR terms
On the right-hand side of the dialog, you should list your regressors in the appropriate edit boxes: • Common coefficients: — enter variables that have the same coefficient across all cross-section members of the pool. EViews will include a single coefficient for each variable, and will label the output using the original expression. • Cross-section specific coefficients: — list variables with different coefficients for each member of the pool. EViews will include a different coefficient for each crosssectional unit, and will label the output using a combination of the cross-section identifier and the series name. • Period specific coefficients: — list variables with different coefficients for each observed period. EViews will include a different coefficient for each period unit, and will label the output using a combination of the period identifier and the series name. For example, if you include the ordinary variable TIME and POP? in the common coefficient list, the output will include estimates for TIME and POP?. If you include these variables in the cross-section specific list, the output will include coefficients labeled “_USA—TIME”, “_UK—TIME”, and “_USA—POP_USA”, “_UK—POP_UK”, etc. Be aware that estimating your model with cross-section or period specific variables may generate large numbers of coefficients. If there are cross-section specific regressors, the number of these coefficients equals the product of the number of pool identifiers and the number of variables in the list; if there are period specific regressors, the number of corresponding coefficients is the number of periods times the number of variables in the list. You may include AR terms in either the common or cross-section coefficients lists. If the terms are entered in the common coefficients list, EViews will estimate the model assuming a common AR error. If the AR terms are entered in the cross-section specific list, EViews will estimate separate AR terms for each pool member. See “Estimating AR Models” on page 89 for a description of AR specifications. Note that EViews only allows specification by list for pool equations. If you wish to estimate a nonlinear specification, you must first create a system object, and then edit the system specification (see “Making a System” on page 583).

Pooled Estimation—589

Fixed and Random Effects
You should account for individual and period effects using the Fixed and Random Effects combo boxes. By default, EViews assumes that there are no effects so that the combo boxes are both set to None. You may change the default settings to allow for either Fixed or Random effects in either the cross-section or period dimension, or both. There are some specifications that are not currently supported. You may not, for example, estimate random effects models with cross-section specific coefficients, AR terms, or weighting. Furthermore, while two-way random effects specifications are supported for balanced data, they may not be estimated in unbalanced designs. Note that when you select a fixed or random effects specification, EViews will automatically add a constant to the common coefficients portion of the specification if necessary, to ensure that the observation weighted sum of the effects is equal to zero.

Weights
By default, all observations are given equal weight in estimation. You may instruct EViews to estimate your specification with estimated GLS weights using the combo box labeled Weights. If you select Cross section weights, EViews will estimate a feasible GLS specification assuming the presence of cross-section heteroskedasticity. If you select Cross-section SUR, EViews estimates a feasible GLS specification correcting for both cross-section heteroskedasticity and contemporaneous correlation. Similarly, Period weights allows for period heteroskedasticity, while Period SUR corrects for both period heteroskedasticity and general correlation of observations within a given cross-section. Note that the SUR specifications are each examples of what is sometimes referred to as the Parks estimator.

590—Chapter 35. Pooled Time Series, Cross-Section Data

Options
Clicking on the Options tab in the dialog brings up a page displaying a variety of estimation options for pool estimation. Settings that are not currently applicable will be grayed out.

Coef Covariance Method
By default, EViews reports conventional estimates of coefficient standard errors and covariances. You may use the combo box at the top of the page to select from the various robust methods available for computing the coefficient standard errors. Each of the methods is described in greater detail in “Robust Coefficient Covariances” on page 611. Note that the checkbox No d.f. correction permits to you compute robust covariances without the leading degree of freedom correction term. This option may make it easier to match EViews results to those from other sources.

Weighting Options
If you are estimating a specification that includes a random effects specification, EViews will provide you with a Random effects method combo box so that you may specify one of the methods for calculating estimates of the component variances. You may choose between the default Swamy-Arora, Wallace-Hussain, or Wansbeek-Kapteyn methods. See “Random Effects” on page 605 for discussion of the differences between the methods. Note that the default Swamy-Arora method should be the most familiar from textbook discussions. Details on these methods are provided in Baltagi (2005), Baltagi and Chang (1994), Wansbeek and Kapteyn (1989). The checkbox labeled Keep GLS weights may be selected to require EViews to save all estimated GLS weights with the equation, regardless of their size. By default, EViews will not save estimated weights in system (SUR) settings, since the size of the required matrix may be quite large. If the weights are not saved with the equation, there may be some pool views and procedures that are not available.

Pooled Estimation—591

Coefficient Name
By default, EViews uses the default coefficient vector C to hold the estimates of the coefficients and effects. If you wish to change the default, simply enter a name in the edit field. If the specified coefficient object exists, it will be used, after resizing if necessary. If the object does not exist, it will be created with the appropriate size. If the object exists but is an incompatible type, EViews will generate an error.

Iteration Control
The familiar Max Iterations and Convergence criterion edit boxes that allow you to set the convergence test for the coefficients and GLS weights. If your specification contains AR terms, the AR starting coefficient values combo box allows you to specify starting values as a fraction of the OLS (with no AR) coefficients, zero, or user-specified values. If Display Settings is checked, EViews will display additional information about convergence settings and initial coefficient values (where relevant) at the top of the regression output. The last set of radio buttons is used to determine the iteration settings for coefficients and GLS weighting matrices. The first two settings, Simultaneous updating and Sequential updating should be employed when you want to ensure that both coefficients and weighting matrices are iterated to convergence. If you select the first option, EViews will, at every iteration, update both the coefficient vector and the GLS weights; with the second option, the coefficient vector will be iterated to convergence, then the weights will be updated, then the coefficient vector will be iterated, and so forth. Note that the two settings are identical for GLS models without AR terms. If you select one of the remaining two cases, Update coefs to convergence and Update coefs once, the GLS weights will only be updated once. In both settings, the coefficients are first iterated to convergence, if necessary, in a model with no weights, and then the weights are computed using these first-stage coefficient estimates. If the first option is selected, EViews will then iterate the coefficients to convergence in a model that uses the first-stage weight estimates. If the second option is selected, the first-stage coefficients will only be iterated once. Note again that the two settings are identical for GLS models without AR terms. By default, EViews will update GLS weights once, and then will update the coefficients to convergence.

592—Chapter 35. Pooled Time Series, Cross-Section Data

Instruments
To estimate a pool specification using instrumental variables techniques, you should select TSLS - Two-Stage Least Squares (and AR) in the Method combo box at the bottom of the main (Specification) dialog page. EViews will respond by creating a three-tab dialog in which the middle tab (page) is used to specify your instruments. As with the regression specification, the instrument list specification is divided into a set of Common, Cross-section specific, and Period specific instruments. The interpretation of these lists is the same as for the regressors; if there are cross-section specific instruments, the number of these instruments equals the product of the number of pool identifiers and the number of variables in the list; if there are period specific instruments, the number of corresponding instruments is the number of periods times the number of variables in the list. Note that you need not specify constant terms explicitly since EViews will internally add constants to the lists corresponding to the specification in the main page. Lastly, there is a checkbox labeled Include lagged regressors for equations with AR terms that will be displayed if your specification includes AR terms. Recall that when estimating an AR specification, EViews performs nonlinear least squares on an AR differenced specification. By default, EViews will add lagged values of the dependent and independent regressors to the corresponding lists of instrumental variables to account for the modified differenced specification. If, however, you desire greater control over the set of instruments, you may uncheck this setting.

Pool Equation Examples
For illustrative purposes, we employ the balanced firm-level data from Grunfeld (1958) that have been used extensively as an example dataset (e.g., Baltagi, 2005). The workfile (“Grunfeld_Baltagi_pool.WF1”) contains annual observations on investement (I?), firm value (F?), and capital stock (K?) for 10 large U.S. manufacturing firms for the 20 years from 1935-54.

Pooled Estimation—593

The pool identifiers for our data are “AR”, “CH”, “DM”, “GE”, “GM”, “GY”, “IB”, “UO”, “US”, “WH”. We obviously cannot demonstrate all of the specifications that may be estimated using these data, but we provide a few illustrative examples.

Fixed Effects
First, we estimate a model regressing I? on the common regressors F? and K?, with a crosssection fixed effect. All regression coefficients are restricted to be the same across all crosssections, so this is equivalent to estimating a model on the stacked data, using the cross-sectional identifiers only for the fixed effect.

The top portion of the output from this regression, which shows the dependent variable, method, estimation and sample information is given by:

EViews displays both the estimates of the coefficients and the fixed effects. Note that EViews automatically includes a constant term so that the fixed effects estimates sum to zero and should be interpreted as deviations from an overall mean. Note also that the estimates of the fixed effects do not have reported standard errors since EViews treats them as nuisance parameters for the purposes of estimation. If you wish to compute standard errors for the cross-section effects, you may estimate a model without a constant and explicitly enter the C in the Cross-section specific coefficients edit field. The bottom portion of the output displays the effects specification and summary statistics for the estimated model.

A few of these summary statistics require discussion. First, the reported R-squared and Fstatistics are based on the difference between the residuals sums of squares from the estimated model, and the sums of squares from a single constant-only specification, not from a fixed-effect-only specification. As a result, the interpretation of these statistics is that they describe the explanatory power of the entire specification, including the estimated fixed effects. Second, the reported information criteria use, as the number of parameters, the number of estimated coefficients, including fixed effects. Lastly, the reported Durbin-Watson stat is formed simply by computing the first-order residual correlation on the stacked set of residuals.

The new output shows the method used for computing the standard errors, and the new standard error estimates, t-statistic values, and probabilities reflecting the robust calculation of the coefficient covariances. Alternatively, we may adopt the Arellano (1987) approach of computing White coefficient covariance estimates that are robust to arbitrary within cross-section residual correlation

We caution that the White period results assume that the number of cross-sections is large, which is not the case in this example. In fact, the resulting coefficient covariance matrix is of reduced rank, a fact that EViews notes in the output.

Note in particular the description of the sample adjustment where we show that the estimation drops one observation for each cross-section when performing the AR differencing, as well as the description of the method used to compute coefficient covariances.

Pooled Estimation—597

Random Effects
Alternatively, we may produce estimates for the two way random effects specification. First, in the Specification page, we set both the cross-section and period effects combo boxes to Random. Note that the dialog changes to show that weighted estimation is not available with random effects (nor is AR estimation). Next, in the Options page we estimate the coefficient covariance using the Ordinary method and we change the Random effects method to use the Wansbeek-Kapteyn method of computing the estimates of the random component variances. Lastly, we click on OK to estimate the model. The top portion of the dialog displays basic information about the specification, including the method used to compute the component variances, as well as the coefficient estimates and associated statistics:
Dependent Variable: I? Method: Pooled EGLS (Two-way random effects) Date: 12/03/03 Time: 14:28 Sample: 1935 1954 Included observations: 20 Number of cross-sections used: 10 Total pool (balanced) observations: 200 Wansbeek and Kapteyn estimator of component variances Variable C F? K? Coefficient -63.89217 0.111447 0.323533 Std. Error 30.53284 0.010963 0.018767 t-Statistic -2.092573 10.16577 17.23947 Prob. 0.0377 0.0000 0.0000

The middle portion of the output (not depicted) displays the best-linear unbiased predictor estimates of the random effects themselves.

Here, we see that the estimated cross-section, period, and idiosyncratic error component standard deviations are 89.26, 15.78, and 51.72, respectively. As seen from the values of Rho, these components comprise 0.73, 0.02 and 0.25 of the total variance. Taking the crosssection component, for example, Rho is computed as:

0.7315 = 89.26257 2 § ( 89.26257 2 + 15.77783 2 + 51.72452 2 )

(35.1)

In addition, EViews reports summary statistics for the random effects GLS weighted data used in estimation, and a subset of statistics computed for the unweighted data.

Cross-section Specific Regressors
Suppose instead that we elect to estimate a specification with I? as the dependent variable, C and F? as the common regressors, and K? as the cross-section specific regressor, using crosssection weighted least squares. The top portion of the output is given by:

Note that EViews displays results for each of the cross-section specific K? series, labeled using the equation identifier followed by the series name. For example, the coefficient labeled “AR--KAR” is the coefficient of KAR in the cross-section equation for firm AR.

Group Dummy Variables
In our last example, we consider the use of the @INGRP pool function to estimate an specification containing group dummy variables (see “Pool Series” on page 570). Suppose we modify our pool definition so that we have defined a group named “MYGROUP” containing the identifiers “GE”, “GM”, and “GY”. We may then estimate a pool specification using the common regressor list:
c f? k? @ingrp(mygrp)

where the latter pool series expression refers to a set of 10 implicit series containing dummy variables for group membership. The implicit series associated with the identifiers “GE”, “GM”, and “GY” will contain the value 1, and the remaining seven series will contain the value 0. The results from this estimation are given by:

We see that the mean value of I? for the three groups is substantially lower than for the remaining groups, and that the difference is statistically significant at conventional levels.

Pool Equation Views and Procedures
Once you have estimated your pool equation, you may examine your output in the usual ways:

Representation
Select View/Representations to examine your specification. EViews estimates your pool as a system of equations, one for each cross-section unit.

Estimation Output
View/Estimation Output will change the display to show the results from the pooled estimation. As with other estimation objects, you can examine the estimates of the coefficient covariance matrix by selecting View/Coef Covariance Matrix.

Testing
EViews allows you to perform coefficient tests on the estimated parameters of your pool equation. Select View/Wald Coefficient Tests… and enter the restriction to be tested. Additional tests are described in the panel discussion “Panel Equation Testing” on page 668

Pooled Estimation—601

Residuals
You can view your residuals in spreadsheet or graphical format by selecting View/Residuals/Table or View/Residuals/Graph. EViews will display the residuals for each cross-sectional equation. Each residual will be named using the base name RES, followed by the cross-section identifier. If you wish to save the residuals in series for later use, select Proc/Make Resids. This procedure is particularly useful if you wish to form specification or hypothesis tests using the residuals.

Residual Covariance/Correlation
You can examine the estimated residual contemporaneous covariance and correlation matrices. Select View/Residual and then either Covariance Matrix or Correlation Matrix to examine the appropriate matrix.

Forecasting
To perform forecasts using a pool equation you will first make a model. Select Proc/Make Model to create an untitled model object that incorporates all of the estimated coefficients. If desired, this model can be edited. Solving the model will generate forecasts for the dependent variable for each of the cross-section units. For further details, see Chapter 34. “Models,” on page 511.

Estimation Background
The basic class of models that can be estimated using a pool object may be written as:

Y it = a + X it ¢b it + d i + g t + e it ,

(35.2)

where Y it is the dependent variable, and X it is a k -vector of regressors, and e it are the error terms for i = 1, 2, º, M cross-sectional units observed for dated periods t = 1, 2, º, T . The a parameter represents the overall constant in the model, while the d i and g t represent cross-section or period specific effects (random or fixed). Identification obviously requires that the b coefficients have restrictions placed upon them. They may be divided into sets of common (across cross-section and periods), cross-section specific, and period specific regressor parameters. While most of our discussion will be in terms of a balanced sample, EViews does not require that your data be balanced; missing values may be used to represent observations that are not available for analysis in a given period. We will detail the unbalanced case only where deemed necessary. We may view these data as a set of cross-section specific regressions so that we have M cross-sectional equations each with T observations stacked on top of one another:

602—Chapter 35. Pooled Time Series, Cross-Section Data

Y i = al T + X i ¢b it + d i l T + I T g + e i

(35.3)

for i = 1, º, M , where l T is a T -element unit vector, I T is the T -element identity matrix, and g is a vector containing all of the period effects, g¢ = ( g 1, g 2, º, g T ) . Analogously, we may write the specification as a set of T period specific equations, each with M observations stacked on top of one another.

Y t = al M + X t ¢b it + I M d + g t l M + e t

(35.4)

for t = 1, º, T , where l M is a M -element unit vector, I M is the M -element identity matrix, and d is a vector containing all of the cross-section effects, d¢ = ( d 1, d 2, º, d M ) . For purposes of discussion we will employ the stacked representation of these equations. First, for the specification organized as a set of cross-section equations, we have:

Y = al MT + Xb + ( I M ƒ l T ) d + ( l M ƒ I T ) g + e

(35.5)

where the matrices b and X are set up to impose any restrictions on the data and parameters between cross-sectional units and periods, and where the general form of the unconditional error covariance matrix is given by:

The remainder of this section describes briefly the various components that you may employ in an EViews pool specification.

Cross-section and Period Specific Regressors
The basic EViews pool specification in Equation (35.2) allows for b slope coefficients that are common to all individuals and periods, as well as coefficients that are either cross-sec-

Pooled Estimation—603

tion or period specific. Before turning to the general specification, we consider three extreme cases. First, if all of the b it are common across cross-sections and periods, we may simplify the expression for Equation (35.2) to:

Y it = a + X it ¢b + d i + g t + e it
There are a total of k coefficients in b , each corresponding to an element of x . Alternately, if all of the b it coefficients are cross-section specific, we have:

(35.9)

Y it = a + X it ¢b i + d i + g t + e it
Note that there are k in each b i for a total of Mk slope coefficients.

(35.10)

Lastly, if all of the b it coefficients are period specific, the specification may be written as:

Y it = a + X it ¢b t + d i + g t + e it
for a total of Tk slope coefficients.

If there are k 1 common regressors, k 2 cross-section specific regressors, and k 3 period specific regressors, there are a total of k 0 = k 1 + k 2 M + k 3 T regressors in b . EViews estimates these models by internally creating interaction variables, M for each regressor in the cross-section regressor list and T for each regressor in the period-specific list, and using them in the regression. Note that estimating models with cross-section or period specific coefficients may lead to the generation of a large number of implicit interaction variables, and may be computationally intensive, or lead to singularities in estimation.

AR Specifications
EViews provides convenient tools for estimating pool specifications that include AR terms. Consider a restricted version of Equation (35.2) on page 601 that does not admit period specific regressors or effects,

Y it = a + X it ¢b i + d i + g t + e it

(35.13)

where the cross-section effect d i is either not present, or is specified as a fixed effect. We then allow the residuals to follow a general AR process:

e it =

r= 1

Â r ri e it – r + h it

p

(35.14)

604—Chapter 35. Pooled Time Series, Cross-Section Data

for all i , where the innovations h it are independent and identically distributed, assuming further that there is no unit root. Note that we allow the autocorrelation coefficients r to be cross-section, but not period specific. If, for example, we assume that e it follows an AR(1) process with cross-section specific AR coefficients, EViews will estimate the transformed equation:

using iterative techniques to estimate ( a, b i, r i ) for all i . See “Estimating AR Models” on page 89 for additional discussion. We emphasize that EViews does place are restrictions on the specifications that admit AR errors. AR terms may not be estimated in specifications with period specific regressors or effects. Lastly, AR terms are not allowed in selected GLS specifications (random effects, period specific heteroskedasticity and period SUR). In those GLS specifications where AR terms are allowed, the error covariance assumption is for the innovations not the autoregressive error.

Fixed and Random Effects
The presence of cross-section and period specific effects terms d and g may be handled using fixed or random effects methods. You may, with some restrictions, specify models containing effects in one or both dimension, for example, a fixed effect in the cross-section dimension, a random effect in the period dimension, or a fixed effect in the cross-section and a random effect in the period dimension. Note, in particular, however, that two-way random effects may only be estimated if the data are balanced so that every cross-section has the same set of observations.

Fixed Effects
The fixed effects portions of specifications are handled using orthogonal projections. In the simple one-way fixed effect specifications and the balanced two-way fixed specification, these projections involve the familiar approach of removing cross-section or period specific means from the dependent variable and exogenous regressors, and then performing the specified regression using the demeaned data (see, for example Baltagi, 2005). More generally, we apply the results from Davis (2002) for estimating multi-way error components models with unbalanced data. Note that if instrumental variables estimation is specified with fixed effects, EViews will automatically add to the instrument list, the constants implied by the fixed effects so that the orthogonal projection is also applied to the instrument list.

Pooled Estimation—605

Random Effects
The random effects specifications assumes that the corresponding effects d i and g t are realizations of independent random variables with mean zero and finite variance. Most importantly, the random effects specification assumes that the effect is uncorrelated with the idiosyncratic residual e it . EViews handles the random effects models using feasible GLS techniques. The first step, estimation of the covariance matrix for the composite error formed by the effects and the residual (e.g., n it = d i + g t + e it in the two-way random effects specification), uses one of the quadratic unbiased estimators (QUE) from Swamy-Arora, Wallace-Hussain, or Wansbeek-Kapteyn. Briefly, the three QUE methods use the expected values from quadratic forms in one or more sets of first-stage estimated residuals to compute moment estimates of the 2 2 2 component variances ( j d , j g, j e ) . The methods differ only in the specifications estimated in evaluating the residuals, and the resulting forms of the moment equations and estimators. The Swamy-Arora estimator of the component variances, cited most often in textbooks, uses residuals from the within (fixed effect) and between (means) regressions. In contrast, the Wansbeek and Kapteyn estimator uses only residuals from the fixed effect (within) estimator, while the Wallace-Hussain estimator uses only OLS residuals. In general, the three should provide similar answers, especially in large samples. The Swamy-Arora estimator requires the calculation of an additional model, but has slightly simpler expressions for the component variance estimates. The remaining two may prove easier to estimate in some settings. Additional details on random effects models are provided in Baltagi (2005), Baltagi and Chang (1994), Wansbeek and Kapteyn (1989). Note that your component estimates may differ slightly from those obtained from other sources since EViews always uses the more complicated unbiased estimators involving traces of matrices that depend on the data (see Baltagi (2005) for discussion, especially “Note 3” on p. 28). Once the component variances have been estimated, we form an estimator of the composite residual covariance, and then GLS transform the dependent and regressor data. If instrumental variables estimation is specified with random effects, EViews will GLS transform both the data and the instruments prior to estimation. This approach to random effects estimation has been termed generalized two-stage least squares (G2SLS). See Baltagi (2005, p. 113-116) and “Random Effects and GLS” on page 609 for additional discussion.

Generalized Least Squares
You may estimate GLS specifications that account for various patterns of correlation between the residuals. There are four basic variance structures that you may specify: crosssection specific heteroskedasticity, period specific heteroskedasticity, contemporaneous covariances, and between period covariances.

606—Chapter 35. Pooled Time Series, Cross-Section Data

Note that all of the GLS specifications described below may be estimated in one-step form, where we estimate coefficients, compute a GLS weighting transformation, and then reestimate on the weighted data, or in iterative form, where to repeat this process until the coefficients and weights converge.

Cross-section Heteroskedasticity
Cross-section heteroskedasticity allows for a different residual variance for each cross section. Residuals between different cross-sections and different periods are assumed to be 0. Thus, we assume that:

E ( e it e it X i∗ ) = j i E ( e is e jt X i∗ ) = 0

2

(35.16)

for all i , j , s and t with i π j and s π t , where X i∗ contains X i and, if estimated by fixed effects, the relevant cross-section or period effects ( d i, g ). Using the cross-section specific residual vectors, we may rewrite the main assumption as:

E ( e i e i ¢ X i∗ ) = j i I T

2

(35.17)

GLS for this specification is straightforward. First, we perform preliminary estimation to obtain cross-section specific residual vectors, then we use these residuals to form estimates of the cross-specific variances. The estimates of the variances are then used in a weighted least squares procedure to form the feasible GLS estimates.

Period Heteroskedasticity
Exactly analogous to the cross-section case, period specific heteroskedasticity allows for a different residual variance for each period. Residuals between different cross-sections and different periods are still assumed to be 0 so that:

E ( e it e jt X t∗ ) = j t E ( e is e jt X t∗ ) = 0

2

(35.18)

for all i , j , s and t with s π t , where X t∗ contains X t and, if estimated by fixed effects, the relevant cross-section or period effects ( d, g t ). Using the period specific residual vectors, we may rewrite the first assumption as:

E ( e t e t ¢ X t∗ ) = j t I M

2

(35.19)

We perform preliminary estimation to obtain period specific residual vectors, then we use these residuals to form estimates of the period variances, reweight the data, and then form the feasible GLS estimates.

Pooled Estimation—607

Contemporaneous Covariances (Cross-section SUR)
This class of covariance structures allows for conditional correlation between the contemporaneous residuals for cross-section i and j , but restricts residuals in different periods to be uncorrelated. Specifically, we assume that:

E ( e it e jt X t∗ ) = j ij E ( e is e jt X t∗ ) = 0

(35.20)

for all i , j , s and t with s π t . The errors may be thought of as cross-sectionally correlated. Alternately, this error structure is sometimes referred to as clustered by period since observations for a given period are correlated (form a cluster). Note that in this specification the contemporaneous covariances do not vary over t . Using the period specific residual vectors, we may rewrite this assumption as,

E ( e t e t ¢ X t∗ ) = Q M
for all t , where,

(35.21)

QM

 j j º j 1M  11 12  j 12 j 22 M =   O  j MM  j M1 º

      

(35.22)

We term this a Cross-section SUR specification since it involves covariances across cross-sections as in a seemingly unrelated regressions type framework (where each equation corresponds to a cross-section). Cross-section SUR generalized least squares on this specification (sometimes referred to as the Parks estimator) is simply the feasible GLS estimator for systems where the residuals are both cross-sectionally heteroskedastic and contemporaneously correlated. We employ residuals from first stage estimates to form an estimate of Q M . In the second stage, we perform feasible GLS. Bear in mind that there are potential pitfalls associated with the SUR/Parks estimation (see Beck and Katz (1995)). For one, EViews may be unable to compute estimates for this model when you the dimension of the relevant covariance matrix is large and there are a small number of observations available from which to obtain covariance estimates. For example, if we have a cross-section SUR specification with large numbers of cross-sections and a small number of time periods, it is quite likely that the estimated residual correlation matrix will be nonsingular so that feasible GLS is not possible.

608—Chapter 35. Pooled Time Series, Cross-Section Data

It is worth noting that an attractive alternative to the SUR methodology estimates the model without a GLS correction, then corrects the coefficient estimate covariances to account for the contemporaneous correlation. See “Robust Coefficient Covariances” on page 611. Note also that if cross-section SUR is combined with instrumental variables estimation, EViews will employ a Generalized Instrumental Variables estimator in which both the data and the instruments are transformed using the estimated covariances. See Wooldridge (2002) for discussion and comparison with the three-stage least squares approach.

Serial Correlation (Period SUR)
This class of covariance structures allows for arbitrary heteroskedasticity and serial correlation between the residuals for a given cross-section, but restricts residuals in different crosssections to be uncorrelated. This error structure is sometimes referred to as clustered by cross-section since observations in a given cross-section are correlated (form a cluster). Accordingly, we assume that:

E ( e is e it X i∗ ) = j st E ( e is e jt X i∗ ) = 0

(35.23)

for all i , j , s and t with i π j . Note that in this specification the heteroskedasticity and serial correlation does not vary across cross-sections i . Using the cross-section specific residual vectors, we may rewrite this assumption as,

E ( e i e i ¢ X i∗ ) = Q T
for all i , where,

(35.24)

QT

 j j º j 1T  11 12  j 12 j 22 M =   O  j TT j T1 º 

      

(35.25)

We term this a Period SUR specification since it involves covariances across periods within a given cross-section, as in a seemingly unrelated regressions framework with period specific equations. In estimating a specification with Period SUR, we employ residuals obtained from first stage estimates to form an estimate of Q T . In the second stage, we perform feasible GLS. See “Contemporaneous Covariances (Cross-section SUR)” on page 607 for related discussion of errors clustered-by-period.

Pooled Estimation—609

Instrumental Variables
All of the pool specifications may be estimated using instrumental variables techniques. In general, the computation of the instrumental variables estimator is a straightforward extension of the standard OLS estimator. For example, in the simplest model, the OLS estimator may be written as:
–1 ˆ b OLS =  Â X i ¢X i  Â X i ¢Y i     i i

where P Z = ( Z i ( Z i ¢Z i ) Z i ¢ ) is the orthogonal projection matrix onto the Z i . i There are, however, additional complexities introduced by instruments that require some discussion.

–1

Cross-section and Period Specific Instruments
As with the regressors, we may divide the instruments into three groups (common instruments Z 0 it , cross-section specific instruments Z 1it , and period specific instruments Z 2it ). You should make certain that any exogenous variables in the regressor groups are included in the corresponding instrument groups, and be aware that each entry in the latter two groups generates multiple instruments.

˜ where Z i = QZ i .
Random Effects and GLS
Similarly, for random effects and other GLS estimators, EViews applies the weighting to the instruments as well as the dependent variable and regressors in the model. For example, with data estimated using cross-sectional GLS, we have:

In the context of random effects specifications, this approach to IV estimation is termed generalized two-stage least squares (G2SLS) method (see Baltagi (2005, p. 113-116) for references and discussion). Note that in implementing the various random effects methods (Swamy-Arora, Wallace-Hussain, Wansbeek-Kapteyn), we have extended the existing results to derive the unbiased variance components estimators in the case of instrumental variables estimation. More generally, the approach may simply be viewed as a special case of the Generalized Instrumental Variables (GIV) approach in which data and the instruments are both transformed using the estimated covariances. You should be aware that this has approach has the effect of altering the implied orthogonality conditions. See Wooldridge (2002) for discussion and comparison with a three-stage least squares approach in which the instruments are not transformed. See “GMM Details” on page 677 for an alternative approach.

AR Specifications
EViews estimates AR specifications by transforming the data to a nonlinear least squares specification, and jointly estimating the original and the AR coefficients. This transformation approach raises questions as to what instruments to use in estimation. By default, EViews adds instruments corresponding to the lagged endogenous and lagged exogenous variables introduced into the specification by the transformation. For example, in an AR(1) specification, we have the original specification,

where Y it – 1 and X it – 1 are introduced by the transformation. EViews will, by default, add these to the previously specified list of instruments Z it . You may, however, instruct EViews not to add these additional instruments. Note, however, that the order condition for the transformed model is different than the order condition for the untransformed specification since we have introduced additional coefficients corresponding to the AR coefficients. If you elect not to add the additional instruments automati-

Pooled Estimation—611

cally, you should make certain that you have enough instruments to account for the additional terms.

Robust Coefficient Covariances
In this section, we describe the basic features of the various robust estimators, for clarity focusing on the simple cases where we compute robust covariances for models estimated by standard OLS without cross-section or period effects. The extensions to models estimated using instrumental variables, fixed or random effects, and GLS weighted least squares are straightforward.

where the leading term is a degrees of freedom adjustment depending on the total number of observations in the stacked data, N∗ is the total number of stacked observations, and and K∗ , the total number of estimated parameters. This estimator is robust to cross-equation (contemporaneous) correlation and heteroskedasticity. Specifically, the unconditional contemporaneous variance matrix E ( e t e t ¢ ) = Q Mt is unrestricted, may now vary with t , with conditional variance matrix E ( e t e t ¢ X t∗ ) that may depend on X t∗ in arbitrary, unknown fashion. See Wooldridge (2002, p. 148-153) and Arellano (1987). Alternatively, the White period method assumes that the errors for a cross-section are heteroskedastic and serially correlated (cross-section clustered). The coefficient covariances are calculated using a White cross-section clustered estimator:

where, in contrast to Equation (35.32), the summations are taken over individuals and individual stacked data instead of periods. The estimator is designed to accommodate arbitrary heteroskedasticity and within cross-section serial correlation. The corresponding multivariate regression (with an equation for each period) allows the unconditional variance matrix E ( e i e i ¢ ) = Q Ti to be unrestricted and varying with i , with conditional variance matrix E ( e i e i ¢ X i∗ ) depending on X i∗ in general fashion.

612—Chapter 35. Pooled Time Series, Cross-Section Data

In contrast, the White (diagonal) method is robust to observation specific heteroskedasticity in the disturbances, but not to correlation between residuals for different observations. The coefficient asymptotic variance is estimated as:

This method allows the unconditional variance matrix E ( ee¢ ) = L to be an unrestricted 2 diagonal matrix, with the conditional variances E(e it X it∗) depending on X it∗ in general fashion. EViews allows you to compute non degree-of-freedom corrected versions of all of the robust coefficient covariance estimators. In these cases, the leading ratio term in the expressions above is dropped from the calculation. While this has no effect on the asymptotic validity of the estimates, it has the practical effect of lowering all of your standard error estimates.

PCSE Robust Covariances
The remaining methods are variants of the first two White statistics in which residuals are replaced by moment estimators for the unconditional variances. These methods, which are variants of the so-called Panel Corrected Standard Error (PCSE) methodology (Beck and Katz, 1995), are robust to unrestricted unconditional variance matrices Q M and Q T , but place additional restrictions on the conditional variance matrices. A sufficient (though not necessary) condition for use of PCSE is that the conditional and unconditional variances are the same. (Note also that as with the SUR estimators above, we require that Q M and Q T not vary with t and i , respectively.) For example, the Cross-section SUR (PCSE) method handles cross-section correlation (period clustering) by replacing the outer product of the cross-section residuals in Equation (35.32) with an estimate of the (contemporaneous) cross-section residual covariance matrix Q M :

Analogously, the Period SUR (PCSE) handles between period correlation (cross-section clustering) by replacing the outer product of the period residuals in Equation (35.33) with an estimate of the period covariance Q T :

The two diagonal forms of these estimators, Cross-section weights (PCSE), and Period ˆ ˆ weights (PCSE), use only the diagonal elements of the relevant Q M and Q T . These covariance estimators are robust to heteroskedasticity across cross-sections or periods, respectively, but not to general correlation of residuals.

References—613

The non degree-of-freedom corrected versions of these estimators remove the leading term involving the number of observations and number of coefficients.

Chapter 36. Working with Panel Data
EViews provides you with specialized tools for working with stacked data that have a panel structure. You may have, for example, data for various individuals or countries that are stacked one on top of another. The first step in working with stacked panel data is to describe the panel structure of your data: we term this step structuring the workfile. Once your workfile is structured as a panel workfile, you may take advantage of the EViews tools for working with panel data, and for estimating equation specifications using the panel structure. The following discussion assumes that you have an understanding of the basics of panel data. “Panel Data,” beginning on page 216 of User’s Guide I provides background on the characteristics of panel structured data. We first review briefly the process of applying a panel structure to a workfile. The remainder of the discussion in this chapter focuses on the basics working with data in a panel workfile. Chapter 37. “Panel Estimation,” on page 647 outlines the features of equation estimation in a panel workfile.

Structuring a Panel Workfile
The first step in panel data analysis is to define the panel structure of your data. By defining a panel structure for your data, you perform the dual tasks of identifying the cross-section associated with each observation in your stacked data, and of defining the way that lags and leads operate in your workfile. While the procedures for structuring a panel workfile outlined below are described in greater detail elsewhere, an abbreviated review may prove useful (for additional detail, see “Describing a Balanced Panel Workfile” on page 38, “Dated Panels” on page 230, and “Undated Panels” on page 235 of User’s Guide I).

616—Chapter 36. Working with Panel Data

There are two basic ways to create a panel structured workfile. First, you may create a new workfile that has a simple balanced panel structure. Simply select File/New/ Workfile... from the main EViews menu to open the Workfile Create dialog. Next, select Balanced Panel from the Workfile structure type combo box, and fill out the dialog as desired. Here, we create a balanced quarterly panel (ranging from 1970Q1 to 2020Q4) with 200 cross-sections. We also enter “Quarterly” in the Page name edit field. When you click on OK, EViews will create an appropriately structured workfile with 40,800 observations (51 years, 4 quarters, 200 cross-sections). You may then enter or import the data into the workfile. More commonly, you will use the second method of structuring a panel workfile, in which you first read stacked data into an unstructured workfile, and then apply a structure to the workfile. While there are a number of issues involved with this operation, let us consider a simple, illustrative example of the basic method.

Structuring a Panel Workfile—617

Suppose that we have data for the job training example considered by Wooldridge (2002), using data from Holzer, et al. (1993), which are provided in “Jtrain.WF1”. These data form a balanced panel of 3 annual observations on 157 firms. The data are first read into a 471 observation, unstructured EViews workfile. The values of the series YEAR and FCODE may be used to identify the date and cross-section, respectively, for each observation. To apply a panel structure to this workfile, simply double click on the “Range:” line at the top of the workfile window, or select Proc/Structure/Resize Current Page... to open the Workfile structure dialog. Select Dated Panel as our Workfile structure type. Next, enter YEAR as the Date series and FCODE as the Cross-section ID series. Since our data form a simple balanced dated panel, we need not concern ourselves with the remaining settings, so we may simply click on OK. EViews will analyze the data in the specified Date series and Cross-section ID series to determine the appropriate structure for the workfile. The data in the workfile will be sorted by cross-section ID series, and then by date, and the panel structure will be applied to the workfile.

618—Chapter 36. Working with Panel Data

Panel Workfile Display
The two most prominent visual changes in a panel structured workfile are the change in the range and sample information display at the top of the workfile window, and the change in the labels used to identify individual observations.

Range and Sample
The first visual change in a panel structured workfile is in the Range and Sample descriptions at the top of workfile window. For a dated panel workfile, EViews will list both the earliest and latest observed dates, the number of crosssections, and the total number of unique observations. Here we see the top portion of an annual workfile with observations from 1935 to 1954 for 10 cross-sections. Note that workfile sample is described using the earliest and latest observed annual frequency dates (“1935 1954”). In contrast, an undated panel workfile will display an observation range of 1 to the total number of observations. The panel dimension statement will indicate the largest number of observations in a cross-section and the number of cross-sections. Here, we have 92 cross-sections containing up to 30 observations, for a total of 506 observations. Note that the workfile sample is described using the raw observation numbers (“1 506”) since there is no notion of a date pair in undated panels.

Panel Workfile Information—619

You may, at any time, click on the Range display line or select Proc/Structure/Resize Current Page... to bring up the Workfile Structure dialog so that you may modify or remove your panel structure.

Observation Labels
The left-hand side of every workfile contains observation labels that identify each observation. In a simple unstructured workfile, these labels are simply the integers from 1 to the total number of observations in the workfile. For dated, non-panel workfiles, these labels are representations of the unique dates associated with each observation. For example, in an annual workfile ranging from 1935 to 1950, the observation labels are of the form “1935”, “1936”, etc. The observation labels in a panel workfile must reflect the fact that observations possess both cross-section and within-cross-section identifiers. Accordingly, EViews will form observation identifiers using both the cross-section and the cell ID values. Here, we see the observation labels in an annual panel workfile formed using the cross-section identifiers and a two-digit year identifier.

Panel Workfile Information
When working with panel data, it is important to keep the basic structure of your workfile in mind at all times. EViews provides you with tools to access information about the structure of your workfile.

Workfile Structure
First, the workfile statistics view provides a convenient place for you to examine the structure of your panel workfile. Simply click on View/Statistics from the main menu to display a summary of the structure and contents of your workfile.

The top portion of the display for our first example workfile is depicted above. The statistics view identifies the page as an annual panel workfile that is structured using the identifiers ID and DATE. There are 10 cross-sections with 20 observations each, for years ranging from 1935 to 1954. For unbalanced data, the number of observations per cross-section reported will be the largest number observed across the cross-sections. To return the display to the original workfile directory, select View/Workfile Directory from the main workfile menu.

Identifier Indices
EViews provides series expressions and functions that provide information about the crosssection, cell, and observation IDs associated with each observation in a panel workfile.

Cross-section Index
The series expression @crossid provides index identifiers for each observation corresponding to the cross-section to which the observation belongs. If, for example, there are 8 observations with cross-section identifier alpha series values (in order), “B”, “A”, “A”, “A”, “B”, “A”, “A”, and “B”, the command:
series cxid = @crossid

assigns a group identifier value of 1 or 2 to each observation in the workfile. Since the panel workfile is sorted by the cross-section ID values, observations with the identifier value “A” will be assigned a CXID value of 1, while “B” will be assigned 2. A one-way tabulation of the CXID series shows the number of observations in each crosssection or group:

Cell Index
Similarly, @cellid may be used to obtain integers uniquely indexing cell IDs. @cellid numbers observations using an index corresponding to the ordered unique values of the cell or date ID values. Note that since the indexing uses all unique values of the cell or date ID series, the observations within a cross-section may be indexed non-sequentially. Suppose, for example, we have a panel workfile with two cross-sections. There are 5 observations in the cross-section “A” with cell ID values “1991”, “1992”, “1993”, “1994”, and “1999”, and 3 observations in the cross-section “B” with cell ID values “1993”, “1996”, “1998”. There are 7 unique cell ID values (“1991”, “1992”, “1993”, “1994”, “1996”, “1998”, “1999”) in the workfile. The series assignment
series cellid = @cellid

will assign to the “A” observations in CELLID the values “1991”, “1992”, “1993”, “1994”, “1997”, and to the “B” observations the values “1993”, “1995”, and “1996”. A one-way tabulation of the CELLID series provides you with information about the number of observations with each index value:

Within Cross-section Observation Index
Alternately, @obsid returns an integer uniquely indexing observations within a cross-section. The observations will be numbered sequentially from 1 through the number of observations in the corresponding cross-section. In the example above, with two cross-section groups “A” and “B” containing 5 and 3 observations, respectively, the command:
series cxid = @crossid series withinid = @obsid

would number the 5 observations in cross-section “A” from 1 through 5, and the 3 observations in group “B” from 1 through 3. Bear in mind that while @cellid uses information about all of the ID values in creating its index, @obsid only uses the ordered observations within a cross-section in forming the index. As a result, the only similarity between observations that share an @obsid value is their ordering within the cross-section. In contrast, observations that share a @cellid value also share values for the underlying cell ID. It is worth noting that if a panel workfile is balanced so that each cross-section has the same cell ID values, @obsid and @cellid yield identical results.

Workfile Observation Index
In rare cases, you may wish to enumerate the observations beginning at

Working with Panel Data—623

the first observation in the first cross-section and ending at the last observation in the last cross-section.
series _id = @obsnum

The @obsnum keyword allows you to number the observations in the workfile in sequential order from 1 to the total number of observations.

Working with Panel Data
For the most part, you will find working with data in a panel workfile to be identical to working with data in any other workfile. There are, however, some differences in behavior that require discussion. In addition, we describe useful approaches to working with panel data using standard, non panel-specific tools.

Lags and Leads
For the most part, expressions involving lags and leads should operate as expected (see “Lags, Leads, and Panel Structured Data” on page 217 of User’s Guide I for a full discussion). In particular note that lags and leads do not cross group boundaries so that they will never involve data from a different cross-section (i.e., lags of the first observation in a crosssection are always NAs, as are leads of the last observation in a cross-section). Since EViews automatically sorts your data by cross-section and cell/date ID, observations in a panel dataset are always stacked by cross-section, with the cell IDs sorted within each cross-section. Accordingly, lags and leads within a cross-section are defined over the sorted values of the cell ID. Lags of an observation are always associated with lower value of the cell ID, and leads always involve a higher value (the first lag observation has the next lowest cell ID value and the first lead has the next highest value). Lags and leads are specified in the usual fashion, using an offset in parentheses. To assign the sum of the first lag of Y and the second lead of X to the series Z, you may use the command:
series z = y(-1) + x(2)

Similarly, you may use lags to obtain the name of the previous child in household cross-sections. The command:
alpha older = childname(-1)

assigns to the alpha series OLDER the name of the preceding observation. Note that since lags never cross over cross-section boundaries, the first value of OLDER in a household will be missing.

624—Chapter 36. Working with Panel Data

Panel Samples
The description of the current workfile sample in the workfile window provides an obvious indication that samples for dated and undated workfiles are specified in different ways.

Dated Panel Samples
For dated workfiles, you may specify panel samples using date pairs to define the earliest and latest dates to be included. For example, in our dated panel example from above, if we issue the sample statement:
smpl 1940 1954

EViews will exclude all observations that are dated from 1935 through 1939. We see that the new sample has eliminated observations for those dates from each cross-section.

As in non-panel workfiles, you may combine the date specification with additional “if” conditions to exclude additional observations. For example:
smpl 1940 1945 1950 1954 if i>50

uses any panel observations that are dated from 1940 to 1945 or 1950 to 1954 that have values of the series I that are greater than 50. Additionally, you may use special keywords to refer to the first and last observations for cross-sections. For dated panels, the sample keywords @first and @last refer to the set of first and last observations for each cross-section. For example, you may specify the sample:
smpl @first 2000

to use data from the first observation in each cross-section and observations up through the end of the year 2000. Likewise, the two sample statements:
smpl @first @first+5 smpl @last-5 @last

use (at most) the first five and the last five observations in each cross-section, respectively. Note that the included observations for each cross-section may begin at a different date, and that:
smpl @all smpl @first @last

are equivalent.

Working with Panel Data—625

The sample statement keywords @firstmin and @lastmax are used to refer to the earliest of the start and latest of the end dates observed over all cross-sections, so that the sample:
smpl @firstmin @firstmin+20

sets the start date to the earliest observed date, and includes the next 20 observations in each cross-section. The command:
smpl @lastmax-20 @lastmax

includes the last observed date, and the previous 20 observations in each cross-section. Similarly, you may use the keywords @firstmax and @lastmin to refer to the latest of the cross-section start dates, and earliest of the end dates. For example, with regular annual data that begin and end at different dates, you may balance the starts and ends of your data using the statement:
smpl @firstmax @lastmin

which sets the sample to begin at the latest observed start date, and to end at the earliest observed end date. The special keywords are perhaps most usefully combined with observation offsets. By adding plus and minus terms to the keywords, you may adjust the sample by dropping or adding observations within each cross-section. For example, to drop the first observation from each cross-section, you may use the sample statement:
smpl @first+1 @last

The following commands generate a series containing cumulative sums of the series X for each cross-section:
smpl @first @first series xsum = x smpl @first+1 @last xsum = xsum(-1) + x

The first two commands initialize the cumulative sum for the first observation in each crosssection. The last two commands accumulate the sum of values of X over the remaining observations. Similarly, if you wish to estimate your equation on a subsample of data and then perform cross-validation on the last 20 observations in each cross-section, you may use the sample defined by,
smpl @first @last-20

to perform your estimation, and the sample,
smpl @last-19 @last

to perform your forecast evaluation.

626—Chapter 36. Working with Panel Data

Note that the processing of sample offsets for each cross-section follows the same rules as for non-panel workfiles “Sample Offsets” on page 95 of User’s Guide I.

Undated Panel Samples
For undated workfiles, you must specify the sample range pairs using observation numbers defined over the entire workfile. For example, in our undated 506 observation panel example, you may issue the sample statement:
smpl 10 500

to drop the first 9 and the last 6 observations in the workfile from the current sample. One consequence of the use of observation pairs in undated panels is that the keywords @first, @firstmin, and @firstmax all refer to observation 1, and @last, @lastmin, and @lastmax, refer to the last observation in the workfile. Thus, in our example, the command:
smpl @first+9 @lastmax-6

will also drop the first 9 and the last 6 observations in the workfile from the current sample. Undated panel sample restrictions of this form are not particularly interesting since they require detailed knowledge of the pattern of observation numbers across those cross-sections. Accordingly, most sample statements in undated workfiles will employ “IF conditions” in place of range pairs. For example, the sample statement,
smpl if townid<>10 and lstat >-.3

is equivalent to either of the commands,
smpl @all if townid<>10 and lstat >-.3 smpl 1 506 if townid<>10 and lstat >-.3

and selects all observations with TOWNID values not equal to 10, and LSTAT values greater than -0.3.

You may combine the sample “IF conditions” with the special functions that return information about the observations in the panel. For example, we may use the @obsid workfile function to identify each observation in a cross-section, so that:
smpl if @obsid>1

drops the first observation for each cross-section.

Working with Panel Data—627

Alternately, to drop the last observation in each cross-section, you may use:
smpl if @obsid < @maxsby(townid, townid, "@all")

The @maxsby function returns the number of non-NA observations for each TOWNID value. Note that we employ the “@ALL” sample to ensure that we compute the @maxsby over the entire workfile sample.

Trends
EViews provides several functions that may be used to construct a time trend in your panel structured workfile. A trend in a panel workfile has the property that the values are initialized at the start of a cross-section, increase for successive observations in the specific crosssection, and are reset at the start of the next cross section. You may use the following to construct your time trend: • The @obsid function may be used to return the simplest notion of a trend in which the values for each cross-section begin at one and increase by one for successive observations in the cross-section. • The @trendc function computes trends in which values for observations with the earliest observed date are normalized to zero, and values for successive observations are incremented based on the calendar associated with the workfile frequency. • The @cellid and @trend functions return time trends in which the values increase based on a calender defined by the observed dates in the workfile. See also “Trend Functions” on page 436 and “Panel Trend Functions” on page 438 of the Command and Programming Reference for discussion.

By-Group Statistics
The “by-group” statistical functions (“By-Group Statistics” on page 406 of the Command and Programming Reference) may be used to compute the value of a statistic for observations in a subgroup, and to assign the computed value to individual observations. While not strictly panel functions, these tools deserve a place in the current discussion since they are well suited for working with panel data. To use the by-group statistical functions in a panel context, you need only specify the group ID series as the classifier series in the function. Suppose, for example, that we have the undated panel structured workfile with the group ID series TOWNID, and that you wish to assign to each observation in the workfile the mean value of LSTAT in the corresponding town. You may perform the series assignment using the command,
series meanlstat = @meansby(lstat, townid, "@all")

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or equivalently,
series meanlstat = @meansby(lstat, @crossid, "@all")

to assign the desired values. EViews will compute the mean value of LSTAT for observations with each TOWNID (or equivalently @crossid, since the workfile is structured using TOWNID) value, and will match merge these values to the corresponding observations. Likewise, we may use the by-group statistics functions to compute the variance of LSTAT or the number of non-NA values for LSTAT for each subgroup using the assignment statements:
series varlstat = @varsby(lstat, townid, "@all") series nalstat = @nasby(lstat, @crossid, "@all")

To compute the statistic over subsamples of the workfile data, simply include a sample string or object as an argument to the by-group statistic, or set the workfile sample prior to issuing the command,
smpl @all if zn=0 series meanlstat1 = @meansby(lstat, @cellid)

In the former example, the by-group function uses the workfile sample to compute the statistic for each cell ID value, while in the latter, the optional argument explicitly overrides the workfile sample. One important application of by-group statistics is to compute the “within” deviations for a series by subtracting off panel group means or medians. The following lines:
smpl @all series withinlstat1 = lstat - @meansby(lstat, townid) series withinlstat2 = lstat - @mediansby(lstat, townid)

compute deviations from the TOWNID specific means and medians. In this example, we omit the optional sample argument from the by-group statistics functions since the workfile sample is previously set to use all observations. Combined with standard EViews tools, the by-group statistics allow you to perform quite complex calculations with little effort. For example, the panel “within” standard deviation for LSTAT may be computed from the single command:
series temp = lstat - @meansby(lstat, townid, "@all") scalar within_std = @stdev(temp)

The first line sets the sample to the first observation in each cross-section. The second line calculates the standard deviation of the group means using the single cross-sectional observations. Note that the group means are calculated over the entire sample. An alternative approach to performing this calculation is described in the next section.

Cross-section and Period Summaries
One of the most important tasks in working with panel data is to compute and save summary data, for example, computing means of a series by cross-section or period. In “ByGroup Statistics” on page 627, we outlined tools for computing by-group statistics using the cross-section ID and match merging them back into the original panel workfile page. Additional tools are available for displaying tables summarizing the by-group statistics or for saving these statistics into new workfile pages. In illustrating these tools, we will work with the familiar Grunfeld data containing data on R&D expenditure and other economic measures for 10 firms for the years 1935 to 1954 (provided in the workfile “Grunfeld_Baltagi.WF1”) These 200 observations form a balanced annual workfile that is structured using the firm number FN as the cross-section ID series, and the date series DATEID to identify the year.

Viewing Summaries
The easiest way to compute by-group statistics is to use the standard by-group statistics view of a series. Simply open the series window for the series of interest and select View/ Descriptive Statistics & Tests/Stats by Classification... to open the Statistics by Classification dialog.

630—Chapter 36. Working with Panel Data

First, you should enter the classifier series in the Series/ Group to classify edit field. Here, we use FN, so that EViews will compute means, standard deviations, and number of observations for each cross-section in the panel workfile. Note that we have unchecked the Group into bins options so that EViews will not combine periods. The result of this computation for the series F is given by:
Descriptive Statistics for F Categorized by values of FN Date: 08/22/06 Time: 15:13 Sample: 1935 1954 Included observations: 200 FN 1 2 3 4 5 6 7 8 9 10 All Mean 4333.845 1971.825 1941.325 693.2100 231.4700 419.8650 149.7900 670.9100 333.6500 70.92100 1081.681 Std. Dev. 904.3048 301.0879 413.8433 160.5993 73.84083 217.0098 32.92756 222.3919 77.25478 9.272833 1314.470 Obs. 20 20 20 20 20 20 20 20 20 20 200

Alternately, to compute statistics for each period in the panel, you should enter “DATEID” instead of “FN” as the classifier series.

Saving Summaries
Alternately, you may wish to compute the by-group panel statistics and save them in their own workfile page. The standard EViews tools for working with workfiles and creating series links make this task virtually effortless.

Working with Panel Data—631

Creating Pages for Summaries
Since we will be computing both by-firm and by-period descriptive statistics, the first step is to create workfile pages to hold the results from our two sets of calculations. The firm page will contain observations corresponding to the unique values of the firm identifier found in the panel page; the annual page will contain observations corresponding to the observed years. To create a page for the firm data, click on the New Page tab in the workfile window, and select Specify by Identifier series.... EViews opens the Workfile Page Create by ID dialog, with the identifiers pre-filled with the series used in the panel workfile structure—the Date series field contains the name of the series used to identify dates in the panel, while the Cross-section ID series field contains the name of the series used to identify firms. The default Method is set to Unique values of ID series from one page, which instructs EViews to simply look at the unique values of the ID series in the specified ID page. Alternately, you may provide multiple pages and take the union or intersection of IDs (Union of common ID series from multiple pages and Intersection of common ID series from multiple pages). You may also elect to create observations associated with the crosses of values for multiple series; the different choices permit you to treat date and non-date series asymmetrically when forming these categories (Cross of two non-date ID series, Cross of one date and one non-date ID series, Cross of ID series with a date range). If you select the latter, the dialog will change, prompting you to specify a frequency, start date and end date. To create a new workfile page using only the values in the FN series, you should delete the Date series specification “DATEID” from the dialog. Next, provide a name for the new page by entering “firm” in the Page edit field. Now click on OK. EViews will examine the FN series to find its unique values, and will create and structure a workfile page to hold those values.

632—Chapter 36. Working with Panel Data

Here, we see the newly created FIRM page and newly created FN series containing the unique values from FN in the other page. Note that the new page is structured as an Undated with ID series page, using the new FN series. Repeating this process using the DATEID series will create an annual page. First click on the original panel page to make it active, then select New Page/Specify by Identifier series... to bring up the previous dialog. Delete the Cross-section ID series specification “FN” from the dialog, provide a name for the new page by entering “annual” in the Page edit field, and click on OK. EViews creates the third page, a regular frequency annual page dated 1935 to 1954.

Computing Summaries using Links
Once the firm and annual pages have been created, it is a simple task to create by-group summaries of the panel data using series links. While links are described elsewhere in greater depth (Chapter 8. “Series Links,” on page 183 of User’s Guide I), we provide a brief description of their use in a panel data context.

Working with Panel Data—633

To create links containing the desired summaries, first click on the original panel page tab to make it active, select one or more series of interest, then right mouse click and select Copy. Next, click on either the firm or the annual page, right mouse click, and select Paste Special.... Alternately, right-click to select the series then drag the selected series onto the tab for the destination page. EViews will open the Link Dialog, prompting you to specify a method for summarizing the data. Suppose, for example, that you select the C01, F, and I series from the panel page and then Paste Special... in the firm page. In this case, EViews analyzes the two pages, and determines that most likely, we wish to match merge the contracted data from the first page into the second page. Accordingly, EViews sets the Merge by setting to General match merge criteria, and prefills the Source ID and Destination ID series with two FN cross-section ID series. The default Contraction method is set to compute the mean values of the series for each value of the ID. You may provide a different pattern to be used in naming the link series, a contraction method, and a sample over which the contraction should be calculated. Here, we create new series with the same names as the originals, computing means over the entire sample in the panel page. Click on OK to All to link all three series into the firm page, yielding:

634—Chapter 36. Working with Panel Data

You may compute other summary statistics by repeating the copy-and-paste-special procedure using alternate contraction methods. For example, selecting the Standard Deviation contraction computes the standard deviation for each cross-section and specified series and uses the linking to merge the results into the firm page. Saving them using the pattern “*SD” will create links named “C01SD”, “FSD”, and “ISD”. Likewise, to compute summary statistics across cross-sections for each year, first create an annual page using New Page/Specify by Identifier series..., then paste-special the panel page series as links in the annual page.

Merging Data into the Panel
To merge data into the panel, simply create links from other pages into the panel page. Linking from the annual page into the panel page will repeat observations for each year across firms. Similarly, linking from the cross-section firm page to the panel page will repeat observations for each firm across all years. In our example, we may link the FSD link from the firm page back into the panel page. Select FSD, switch to the panel page, and paste-special. Click OK to accept the defaults in the Paste Special dialog. EViews match merges the data from the firm page to the panel page, matching FN values. Since the merge is from one-to-many, EViews simply repeats the values of FSD in the panel page.

Basic Panel Analysis—635

Basic Panel Analysis
EViews provides various degrees of support for the analysis of data in panel structured workfiles. There is a small number of panel-specific analyses that are provided for data in panel structured workfiles. You may use EViews special tools for graphing dated panel data, perform unit root or cointegration tests, or estimate various panel equation specifications. Alternately, you may apply EViews standard tools for by-group analysis to the stacked data. These tools do not use the panel structure of the workfile, per se, but used appropriately, the by-group tools will allow you to perform various forms of panel analysis. In most other cases, EViews will simply treat panel data as a set of stacked observations. The resulting stacked analysis correctly handles leads and lags in the panel structure, but does not otherwise use the cross-section and cell or period identifiers in the analysis.

Panel-Specific Analysis
Time Series Graphs
EViews provides tools for displaying time series graphs with panel data. You may use these tools to display a graph of the stacked data, individual or combined graphs for each crosssection, or a time series graph of summary statistics for each period. To display panel graphs for a series or group of series in a dated workfile, open the series or group window and click on View/Graph... to bring up the Graph Options dialog. In the Panel options section on the lower right of the dialog, EViews offers you a variety of choices for how you wish to display the data.

636—Chapter 36. Working with Panel Data

Here we see the dialog for graphing a single series. Note in particular the panel workfile specific Panel options section which controls how the multiple cross-sections in your panel should be handled. If you select Stack cross sections EViews will display a single graph of the stacked data, labeled with both the cross-section and date. For example, with a Line & Symbol type graph, we have

Alternately, selecting Individual cross sections displays separate time series graphs for each cross-section, while Combined cross sections displays separate lines for each cross-

Basic Panel Analysis—637

section in a single graph. We caution you that both types of panel graphs may become difficult to read when there are large numbers of cross-sections. For example, the individual graphs for the 10 cross-section panel data depicted here provide information on general trends, but little in the way of detail:

Nevertheless, the graph does offer you the ability examine all of your cross-sections at-aglance. The remaining two options allow you to plot a single graph containing summary statistics for each period. For line graphs, you may select Mean plus SD bounds, and then use the drop down menu on the lower right to choose between displaying no bounds, and 1, 2, or 3 standard deviation bounds. For other graph types such as area or spike, you may only display the means of the data by period. For line graphs you may select Median plus quantiles, and then use the drop down menu to choose additional extreme quantiles to be displayed. For other graph types, only the median may be plotted. Suppose, for example, that we display a line graph containing the mean and 2 standard deviation bounds for the F series. EViews computes, for each period, the mean and standard deviation of F across cross-sections, and displays these in a time series graph:

638—Chapter 36. Working with Panel Data

Similarly, we may display a spike graph of the medians of F for each period:

Displaying graph views of a group object in a panel workfile involves similar choices about the handling of the panel structure.

Panel Unit Root Tests
EViews provides convenient tools for computing panel unit root tests. You may compute one or more of the following tests: Levin, Lin and Chu (2002), Breitung (2000), Im, Pesaran and Shin (2003), Fisher-type tests using ADF and PP tests—Maddala and Wu (1999), Choi (2001), and Hadri (2000). These tests are described in detail in “Panel Unit Root Test,” beginning on page 391.

Basic Panel Analysis—639

To compute the unit root test on a series, simply select View/ Unit Root Test…from the menu of a series object. By default, EViews will compute a Summary of all of the first five unit root tests, where applicable, but you may use the combo box in the upper left hand corner to select an individual test statistic. In addition, you may use the dialog to specify trend and intercept settings, to specify lag length selection, and to provide details on the spectral estimation used in computing the test statistic or statistics. To begin, we open the F series in our example panel workfile, and accept the defaults to compute the summary of several unit root tests on the level of F. The results are given by
Panel unit root test: Summary Date: 08/22/06 Time: 17:05 Sample: 1935 1954 Exogenous variables: Individual effects User specified lags at: 1 Newey-West bandwidth selection using Bartlett kernel Balanced observations for each test Crosssections 10

** Probabilities for Fisher tests are computed using an asympotic Chi -square distribution. All other tests assume asymptotic normality.

Note that there is a fair amount of disagreement in these results as to whether F has a unit root, even within tests that evaluate the same null hypothesis (e.g., Im, Pesaran and Shin vs. the Fisher ADF and PP tests).

Panel Cointegration Tests
EViews provides a number of procedures for computing panel cointegration tests. The following tests are available in EViews: Pedroni (1999, 2004), Kao (1999) and Fisher-type test using Johansen’s test methodology (Maddala and Wu (1999)). The details of these tests are described in “Panel Cointegration Details,” beginning on page 700. To compute a panel cointegration test, select View/Cointegration Test/Panel Cointegration Test… from the menu of an EViews group. You may use various options for specifying the trend specification, lag length selection and spectral estimation methods. To illustrate, we perform a Pedroni panel cointegration test. The only modification from the default settings that we make is to select Automatic selection for lag length. Click on OK to accept the settings and perform the test.

The top portion of the output indicates the type of test, null hypothesis, exogenous variables, and other test options. The next section provides several Pedroni panel cointegration test statistics which evaluate the null against both the homogeneous and the heterogeneous alternatives. In this case, eight of the eleven statistics do not reject the null hypothesis of no cointegration at the conventional size of 0.05. The bottom portion of the table reports auxiliary cross-section results showing intermediate calculating used in forming the statistics. For the Pedroni test this section is split into two sections. The first section contains the Phillips-Perron non-parametric results, and the second section presents the Augmented Dickey-Fuller parametric results.

In addition, if your sample consists of a single cross-section, you may perform a cointegration test on the single cross-section using the general tools described in Chapter 38. “Cointegration Testing,” on page 685. Simply select View/Cointegration Test/Individual Johansen Cointegration Test… or View/Cointegration Test/Individual Single-Equation Cointegration Test… to compute the appropriate test. Both of these methods will generate an error message if your sample contains more than one cross-section.

Stacked By-Group Analysis
There are various by-group analysis tools that may be used to perform analysis of panel data. Previously, we considered an example of using by-group tools to examine data in “Cross-section and Period Summaries” on page 629. Standard by-group views may also be to test for equality of means, medians, or variances between groups, or to examine boxplots by cross-section or period.

Basic Panel Analysis—643

For example, to compute a test of equality of means for F between firms, simply open the series, then select View/Descriptive Statistics & Tests/Equality Tests by Classification.... Enter FN in the Series/Group for Classify edit field, and select OK to continue. EViews will compute and display the results for an ANOVA for F, classifying the data by firm ID. The top portion of the ANOVA results is given by:
Test for Equality of Means of F Categorized by values of FN Date: 08/22/06 Time: 17:11 Sample: 1935 1954 Included observations: 200 Method Anova F-test Welch F-test* df (9, 190) (9, 71.2051) Value 293.4251 259.3607 Probability 0.0000 0.0000

Note in this example that we have relatively few cross-sections with moderate numbers of observations in each firm. Data with very large numbers of group identifiers and few observations are not recommended for this type of testing. To test equality of means between periods, call up the dialog and enter either YEAR or DATEID as the series by which you will classify.

644—Chapter 36. Working with Panel Data

A graphical summary of the primary information in the ANOVA may be obtained by displaying boxplots by cross-section or period. For moderate numbers of distinct classifier values, the graphical display may prove informative. Select View/Graph... to bring up the Graph Options dialog. Select Categorical graph from the drop down on the top left, select Boxplot from the list of graph types, and enter FN in the Within graph edit field. Click OK to display the boxplots using the default settings.

Stacked Analysis
A wide range of analyses are available in panel structured workfiles that have not been specifically redesigned to use the panel structure of your data. These tools allow you to work with and analyze the stacked data, while taking advantage of the support for handling lags and leads in the panel structured workfile. We may, for example, take our example panel workfile, create a group containing the series C01, F, and the expression I+I(-1), and then select View/Descriptive Stats/Individual Samples from the group menu. EViews displays the descriptive statistics for the stacked data. Note that the calculations are performed over the entire 200 observation stacked data, and that the statistics for I+I(-1) use only 190 observations (200 minus 10 observations corresponding to the lag of the first observation for each firm).

References—645

Similarly, suppose you wish to perform a hypothesis testing on a single series. Open the window for the series F, and select View/ Descriptive Statistics & Tests/ Simple Hypothesis Tests.... Enter “120” in the edit box for testing the mean value of the stacked series against a null of 120. EViews displays the results of a simple hypothesis test for the mean of the 200 observation stacked data. While a wide variety of stacked analyses are supported, various views and procedures are not available in panel structured workfiles. You may not, for example, perform seasonal adjustment or estimate VAR or VEC models with the stacked panel.

Chapter 37. Panel Estimation
EViews allows you to estimate panel equations using linear or nonlinear squares or instrumental variables (two-stage least squares), with correction for fixed or random effects in both the cross-section and period dimensions, AR errors, GLS weighting, and robust standard errors. In addition, GMM tools may be used to estimate most of the these specifications with various system-weighting matrices. Specialized forms of GMM also allow you to estimate dynamic panel data specifications. Note that all of the estimators described in this chapter require a panel structured workfile (“Structuring a Panel Workfile” on page 615). We begin our discussion by briefly outlining the dialog settings associated with common panel equation specifications. While the wide range of models that EViews supports means that we cannot exhaustively describe all of the settings and specifications, we hope to provide you a roadmap of the steps you must take to estimate your panel equation. More useful, perhaps, is the discussion that follows, which follows the estimation of some simple panel examples, and describes the use of the wizard for specifying dynamic panel data models. A background discussion of the supported techniques is provided in “Estimation Background” in ”Pooled Estimation” on page 601, and in “Estimation Background,” beginning on page 676.

Estimating a Panel Equation
The first step in estimating a panel equation is to call up an equation dialog by clicking on Object/New Object.../Equation or Quick/Estimate Equation… from the main menu, or typing the keyword equation in the command window. You should make certain that your workfile is structured as a panel workfile. EViews will detect the presence of your panel structure and in place of the standard equation dialog will open the panel Equation Estimation dialog. You should use the Method combo box to choose between LS - Least Squares (LS and AR), TSLS - Two-Stage Least Squares (TSLS and AR), and GMM / DPD - Generalized Method of Moments / Dynamic Panel Data techniques. If you select the either of the latter two methods, the dialog will be updated to provide you with an additional page for specifying instruments (see “Instrumental Variables Estimation” on page 650). The remaining estimation supported estimation techniques do not account for the panel structure of your workfile, save for lags not crossing the boundaries between cross-section units.

648—Chapter 37. Panel Estimation

Least Squares Estimation
The basic least squares estimation dialog is a multi-page dialog with pages for the basic specification, panel estimation options, and general estimation options.

Least Squares Specification
You should provide an equation specification in the upper Equation specification edit box, and an estimation sample in the Sample edit box. The equation may be specified by list or by expression as described in “Specifying an Equation in EViews” on page 6. In general, most of the specifications allowed in nonpanel equation settings may also be specified here. You may, for example, include AR terms in both linear and nonlinear specifications, and may include PDL terms in equations specified by list. You may not, however, include MA terms in a panel setting.

Least Squares Panel Options
Next, click on the Panel Options tab to specify additional panel specific estimation settings. First, you should account for individual and period effects using the Effects specification combo boxes. By default, EViews assumes that there are no effects so that both combo boxes are set to None. You may change the default settings to allow for either Fixed or Random effects in either the cross-sec-

Estimating a Panel Equation—649

tion or period dimension, or both. See the pool discussion of “Fixed and Random Effects” on page 604 for details. You should be aware that when you select a fixed or random effects specification, EViews will automatically add a constant to the common coefficients portion of the specification if necessary, to ensure that the effects sum to zero. Next, you should specify settings for GLS Weights. You may choose to estimate with no weighting, or with Cross-section weights, Cross-section SUR, Period weights, Period SUR. The Cross-section SUR setting allows for contemporaneous correlation between cross-sections (clustering by period), while the Period SUR allows for general correlation of residuals across periods for a specific cross-section (clustering by individual). Cross-section weights and Period weights allow for heteroskedasticity in the relevant dimension. For example, if you select Cross section weights, EViews will estimate a feasible GLS specification assuming the presence of cross-section heteroskedasticity. If you select Cross-section SUR, EViews estimates a feasible GLS specification correcting for heteroskedasticity and contemporaneous correlation. Similarly, Period weights allows for period heteroskedasticity, while Period SUR corrects for heteroskedasticity and general correlation of observations within a cross-section. Note that the SUR specifications are both examples of what is sometimes referred to as the Parks estimator. See the pool discussion of “Generalized Least Squares” on page 605 for additional details. Lastly, you should specify a method for computing coefficient covariances. You may use the combo box labeled Coef covariance method to select from the various robust methods available for computing the coefficient standard errors. The covariance calculations may be chosen to be robust under various assumptions, for example, general correlation of observations within a cross-section, or perhaps cross-section heteroskedasticity. Click on the checkbox No d.f. correction to perform the calculations without the leading degree of freedom correction term. Each of the coefficient covariance methods is described in greater detail in “Robust Coefficient Covariances” on page 611 of the pool chapter. You should note that some combinations of specifications and estimation settings are not currently supported. You may not, for example, estimate random effects models with crosssection specific coefficients, AR terms, or weighting. Furthermore, while two-way random effects specifications are supported for balanced data, they may not be estimated in unbalanced designs.

650—Chapter 37. Panel Estimation

LS Options
Lastly, clicking on the Options tab in the dialog brings up a page displaying computational options for panel estimation. Settings that are not currently applicable will be grayed out. These options control settings for derivative taking, random effects component variance calculation, coefficient usage, iteration control, and the saving of estimation weights with the equation object. These options are identical to those found in pool equation estimation, and are described in considerable detail in “Options” on page 590.

Instrumental Variables Estimation
To estimate a pool specification using instrumental variables techniques, you should select TSLS - Two-Stage Least Squares (and AR) in the Method combo box at the bottom of the main (Specification) dialog page. EViews will respond by creating a four page dialog in which the third page is used to specify your instruments. While the three original pages are unaffected by this choice of estimation method, note the presence of the new third dialog page labeled Instruments, which you will use to specify your instruments. Click on the Instruments tab to display the new page.

IV Instrument Specification
There are only two parts to the instrumental variables page. First, in the edit box

Estimating a Panel Equation—651

labeled Instrument list, you will list the names of the series or groups of series you wish to use as instruments. Next, if your specification contains AR terms, you should use the checkbox to indicate whether EViews should automatically create instruments to be used in estimation from lags of the dependent and regressor variables in the original specification. When estimating an equation specified by list that contains AR terms, EViews transforms the linear model and estimates the nonlinear differenced specification. By default, EViews will add lagged values of the dependent and independent regressors to the corresponding lists of instrumental variables to account for the modified specification, but if you wish, you may uncheck this option. See the pool chapter discussion of “Instrumental Variables” on page 609 for additional detail.

GMM Estimation
To estimate a panel specification using GMM techniques, you should select GMM / DPD Generalized Method of Moments / Dynamic Panel Data in the Method combo box at the bottom of the main (Specification) dialog page. Again, you should make certain that your workfile has a panel structure. EViews will respond by displaying a four page dialog that differs significantly from the previous dialogs.

GMM Specification
The specification page is similar to the earlier dialogs. As in the earlier dialogs, you will enter your equation specification in the upper edit box and your sample in the lower edit box. Note, however, the presence of the Dynamic Panel Wizard... button on the bottom of the dialog. Pressing this button opens a wizard that will aid you in filling out the dialog so that you may employ dynamic panel data techniques such as the Arellano-Bond 1-step estimator for models with lagged endogenous variables and cross-section fixed effects. We will return to this wizard shortly (“GMM Example” on page 663).

652—Chapter 37. Panel Estimation

GMM Panel Options
Next, click on the Panel Options dialog to specify additional settings for your estimation procedure. As before, the dialog allows you to indicate the presence of cross-section or period fixed and random effects, to specify GLS weighting, and coefficient covariance calculation methods. There are, however, notable changes in the available settings. First, when estimating with GMM, there are two additional choices for handling cross-section fixed effects. These choices allow you to indicate a transformation method for eliminating the effect from the specification. You may select Difference to indicate that the estimation procedure should use first differenced data (as in Arellano and Bond, 1991), and you may use Orthogonal Deviations (Arellano and Bover, 1995) to perform an alternative method of removing the individual effects. Second, the dialog presents you with a new combo box so that you may specify weighting matrices that may provide for additional efficiency of GMM estimation under appropriate assumptions. Here, the available options depend on other settings in the dialog. In most cases, you may select a method that computes weights under one of the assumptions associated with the robust covariance calculation methods (see “Least Squares Panel Options” on page 648). If you select White cross-section, for example, EViews uses GMM weights that are formed assuming that there is contemporaneous correlation between cross-sections. If, however, you account for cross-section fixed effects by performing first difference estimation, EViews provides you with a modified set of GMM weights choices. In particular, the Difference (AB 1-step) weights are those associated with the difference transformation. Selecting these

Estimating a Panel Equation—653

weights allows you to estimate the GMM specification typically referred to as Arellano-Bond 1-step estimation. Similarly, you may choose the White period (AB 1-step) weights if you wish to compute Arellano-Bond 2-step or multi-step estimation. Note that the White period weights have been relabeled to indicate that they are typically associated with a specific estimation technique. Note also that if you estimate your model using difference or orthogonal deviation methods, some GMM weighting methods will no longer be available.

GMM Instruments
Instrument specification in GMM estimation follows the discussion above with a few additional complications. First, you may enter your instrumental variables as usual by providing the names of series or groups in the edit field. In addition, you may tag instruments as period-specific predetermined instruments, using the @dyn keyword, to indicate that the number of implied instruments expands dynamically over time as additional predetermined variables become available. To specify a set of dynamic instruments associated with the series X, simply enter “@DYN(X)” as an instrument in the list. EViews will, by default, use the series X(-2), X(-3), ..., X(-T), as instruments for each period (where available). Note that the default set of instruments grows very quickly as the number of periods increases. With 20 periods, for example, there are 171 implicit instruments associated with a single dynamic instrument. To limit the number of implied instruments, you may use only a subset of the instruments by specifying additional arguments to @dyn describing a range of lags to be used. For example, you may limit the maximum number of lags to be used by specifying both a minimum and maximum number of lags as additional arguments. The instrument specification:
@dyn(x, -2, -5)

instructs EViews to include lags of X from 2 to 5 as instruments for each period. If a single argument is provided, EViews will use it as the minimum number of lags to be considered, and will include all higher ordered lags. For example:
@dyn(x, -5)

includes available lags of X from 5 to the number of periods in the sample. Second, in specifications estimated using transformations to remove the cross-section fixed effects (first differences or orthogonal deviations), use may use the @lev keyword to instruct EViews to use the instrument in untransformed, or level form. Tagging an instrument with “@LEV” indicates that the instrument is for the transformed equation If @lev is not provided, EViews will transform the instrument to match the equation transformation.

654—Chapter 37. Panel Estimation

If, for example, you estimate an equation that uses orthogonal deviations to remove a crosssection fixed effect, EViews will, by default, compute orthogonal deviations of the instruments provided prior to their use. Thus, the instrument list:
z1 z2 @lev(z3)

will use the transformed Z1 and Z2, and the original Z3 as the instruments for the specification. Note that in specifications where @dyn and @lev keywords are not relevant, they will be ignored. If, for example, you first estimate a GMM specification using first differences with both dynamic and level instruments, and then re-estimate the equation using LS, EViews will ignore the keywords, and use the instruments in their original forms.

GMM Options
Lastly, clicking on the Options tab in the dialog brings up a page displaying computational options for GMM estimation. These options are virtually identical to those for both LS and IV estimation (see “LS Options” on page 650). The one difference is in the option for saving estimation weights with the object. In the GMM context, this option applies to both the saving of GLS as well as GMM weights.

Panel Estimation Examples
Least Squares Examples
To illustrate the estimation of panel equations in EViews, we first consider an example involving unbalanced panel data from Harrison and Rubinfeld (1978) for the study of hedonic pricing (“Harrison_panel.WF1”). The data are well known and used as an example dataset in many sources (e.g., Baltagi (2005), p. 171). The data consist of 506 census tract observations on 92 towns in the Boston area with group sizes ranging from 1 to 30. The dependent variable of interest is the logarithm of the median value of owner occupied houses (MV), and the regressors include various measures of housing desirability. We begin our example by structuring our workfile as an undated panel. Click on the “Range:” description in the workfile window, select Undated Panel, and enter “TOWNID” as the Identifier series. EViews will prompt you twice to create a CELLID series to uniquely identify observations. Click on OK to both questions to accept your settings.

Panel Estimation Examples—655

EViews restructures your workfile so that it is an unbalanced panel workfile. The top portion of the workfile window will change to show the undated structure which has 92 cross-sections and a maximum of 30 observations in a cross-section. Next, we open the equation specification dialog by selecting Quick/Estimate Equation from the main EViews menu. First, following Baltagi and Chang (1994) (also described in Baltagi, 2005), we estimate a fixed effects specification of a hedonic housing equation. The dependent variable in our specification is the median value MV, and the regressors are the crime rate (CRIM), a dummy variable for the property along Charles River (CHAS), air pollution (NOX), average number of rooms (RM), proportion of older units (AGE), distance from employment centers (DIS), proportion of African-Americans in the population (B), and the proportion of lower status individuals (LSTAT). Note that you may include a constant term C in the specification. Since we are estimating a fixed effects specification, EViews will add one if it is not present so that the fixed effects estimates are relative to the constant term and add up to zero. Click on the Panel Options tab and select Fixed for the Cross-section effects. To match the Baltagi and Chang results, we will leave the remaining settings at their defaults. Click on OK to accept the specification.

The results for the fixed effects estimation are depicted here. Note that as in pooled estimation, the reported R-squared and F-statistics are based on the difference between the residuals sums of squares from the estimated model, and the sums of squares from a single constant-only specification, not from a fixed-effect-only specification. Similarly, the reported information criteria report likelihoods adjusted for the number of estimated coefficients, including fixed effects. Lastly, the reported Durbin-Watson stat is formed simply by computing the first-order residual correlation on the stacked set of residuals. We may click on the Estimate button to modify the specification to match the Wallace-Hussain random effects specification considered by Baltagi and Chang. We modify the specification to include the additional regressors (ZN, INDUS, RAD, TAX, PTRATIO) used in estimation, change the cross-section effects to be estimated as a random effect, and use the Options page to set the random effects computation method to Wallace-Hussain. The top portion of the resulting output is given by:

Note that the estimates of the component standard deviations must be squared to match the component variances reported by Baltagi and Chang (0.016 and 0.020, respectively). Next, we consider an example of estimation with standard errors that are robust to serial correlation. For this example, we employ data on job training grants (“Jtrain.WF1”) used in examples from Wooldridge (2002, p. 276 and 282). As before, the first step is to structure the workfile as a panel workfile. Click

658—Chapter 37. Panel Estimation

on Range: to bring up the dialog, and enter “YEAR” as the date identifier and “FCODE” as the cross-section ID. EViews will structure the workfile so that it is a panel workfile with 157 cross-sections, and three annual observations. Note that even though there are 471 observations in the workfile, a large number of them contain missing values for variables of interest. To estimate the fixed effect specification with robust standard errors (Wooldridge example 10.5, p. 276), click on specification Quick/Estimate Equation from the main EViews menu. Enter the list specification:
lscrap c d88 d89 grant grant_1

in the Equation specification edit box on the main page and select Fixed in the Cross-section effects specification combo box on the Panel Options page. Lastly, since we wish to compute standard errors that are robust to serial correlation (Arellano (1987), White (1980)), we choose White period as the Coef covariance method. To match the reported Wooldridge example, we must select No d.f. correction in the covariance calculation. Click on OK to accept the options. EViews displays the results from estimation:

Note that EViews automatically adjusts for the missing values in the data. There are only 162 observations on 54 cross-sections used in estimation. The top portion of the output indicates that the results use robust White period standard errors with no d.f. correction. Notice that EViews warns you that the estimated coefficient covariances is not of full rank. Alternately, we may estimate a first difference estimator for these data with robust standard errors (Wooldridge example 10.6, p. 282). Open a new equation dialog by clicking on Quick/Estimate Equation..., or modify the existing equation by clicking on the Estimate button on the equation toolbar. Enter the specification:
d(lscrap) c d89 d(grant) d(grant_1)

in the Equation specification edit box on the main page, select None in the Cross-section effects specification combo box, White period and No d.f. correction for the coefficient covariance method on the Panel Options page. The results are given by:

While current versions of EViews do not provide a full set of specification tests for panel equations, it is a straightforward task to construct some tests using residuals obtained from the panel estimation. To continue with the Wooldridge example, we may test for AR(1) serial correlation in the first-differenced equation by regressing the residuals from this specification on the lagged residuals using data for the year 1989. First, we save the residual series in the workfile. Click on Proc/Make Residual Series... on the estimated equation toolbar, and save the residuals to the series RESID01. Next, regress RESID01 on RESID01(-1), yielding:

Under the null hypothesis that the original idiosyncratic errors are uncorrelated, the residuals from this equation should have an autocorrelation coefficient of -0.5. Here, we obtain an ˆ estimate of r 1 = 0.237 which appears to be far from the null value. A formal Wald hypothesis test rejects the null that the original idiosyncratic errors are serially uncorrelated. Perform a Wald test on the test equation by clicking on View/Coefficient Diagnostics/ Wald-Coefficient Restrictions... and entering the restriction “C(1)=-0.5” in the edit box:
Wald Test: Equation: Untitled Null Hyp othesis: C(1)=-0.5 Test Stati stic t-statistic F-statisti c Chi-squa re Value 5.525812 30.53460 30.53460 df 53 (1, 53) 1 Probability 0.0000 0.0000 0.0000

Instrumental Variables Example
To illustrate the estimation of instrumental variables panel estimators, we consider an example taken from Papke (1994) for enterprise zone data for 22 communities in Indiana that is outlined in Wooldridge (2002, p. 306).

662—Chapter 37. Panel Estimation

The panel workfile for this example is structured using YEAR as the period identifier, and CITY as the cross-section identifier. The result is a balanced annual panel for dates from 1980 to 1988 for 22 cross-sections. To estimate the example specification, create a new equation by entering the keyword tsls in the command line, or by clicking on Quick/Estimate Equation... in the main menu. Selecting TSLS - Two-Stage Least Squares (and AR) in the Method combo box to display the instrumental variables estimator dialog, if necessary, and enter:
d(luclms) c d(luclms(-1)) d(ez)

to regress the difference of log unemployment claims (LUCLMS) on the lag difference, and the difference of enterprise zone designation (EZ). Since the model is estimated with time intercepts, you should click on the Panel Options page, and select Fixed for the Period effects. Next, click on the Instruments tab, and add the names:
c d(luclms(-2)) d(ez)

to the Instrument list edit box. Note that adding the constant C to the regressor and instrument boxes is not required since the fixed effects estimator will add it for you. Click on OK to accept the dialog settings. EViews displays the output for the IV regression:

Note that the instrument rank in this equation is 8 since the period dummies also serve as instruments, so you have the 3 instruments specified explicitly, plus 5 for the non-collinear period dummy variables.

GMM Example
To illustrate the estimation of dynamic panel data models using GMM, we employ the unbalanced 1031 observation panel of firm level data (“Abond_pan.WF1”) from Layard and Nickell (1986), previously examined by Arellano and Bond (1991). The analysis fits the log of employment (N) to the log of the real wage (W), log of the capital stock (K), and the log of industry output (YS).

664—Chapter 37. Panel Estimation

The workfile is structured as a dated annual panel using ID as the cross-section identifier series and YEAR as the date classification series. Since the model is assumed to be dynamic, we employ EViews tools for estimating dynamic panel data models. To bring up the GMM dialog, enter the keyword gmm in the command line, or select Quick/Estimate Equation... from the main menu, and choose GMM/DPD - Generalized Method of Moments / Dynamic Panel Data in the Method combo box to display the IV estimator dialog. Click on the button labeled Dynamic Panel Wizard... to bring up the DPD wizard. The DPD wizard is a tool that will aid you in filling out the general GMM dialog. The first page is an introductory screen describing the basic purpose of the wizard. Click Next to continue. The second page of the wizard prompts you for the dependent variable and the number of its lags to include as explanatory variables. In this example, we wish to estimate an equation with N as the dependent variable and N(-1) and N(-2) as explanatory variables so we enter “N” and select “2” lags in the combo box. Click on Next to continue to the next page, where you will specify the remaining explanatory variables. In the next page, you will complete the specification of your explanatory variables. First, enter the list:
w w(-1) k ys ys(-1)

in the regressor edit box to include these variables. Since the desired specification will include time dummies, make certain that the checkbox for Include period dummy variables is selected, then click on Next to proceed.

Panel Estimation Examples—665

The next page of the wizard is used to specify a transformation to remove the cross-section fixed effect. You may choose to use first Differences or Orthogonal deviations. In addition, if your specification includes period dummy variables, there is a checkbox asking whether you wish to transform the period dummies, or to enter them in levels. Here we specify the first difference transformation, and choose to include untransformed period dummies in the transformed equation. Click on Next to continue. The next page is where you will specify your dynamic period-specific (predetermined) instruments. The instruments should be entered with the “@DYN” tag to indicate that they are to be expanded into sets of predetermined instruments, with optional arguments to indicate the lags to be included. If no arguments are provided, the default is to include all valid lags (from -2 to “-infinity”). Here, we instruct EViews that we wish to use the default lags for N as predetermined instruments.

666—Chapter 37. Panel Estimation

You should now specify the remaining instruments. There are two lists that should be provided. The first list, which is entered in the edit field labeled Transform, should contain a list of the strictly exogenous instruments that you wish to transform prior to use in estimating the transformed equation. The second list, which should be entered in the No transform edit box should contain a list of instruments that should be used directly without transformation. Enter the remaining instruments:
w w(-1) k ys ys(-1)

in the first edit box and click on Next to proceed to the final page. The final page allows you to specify your GMM weighting and coefficient covariance calculation choices. In the first combo box, you will choose a GMM Iteration option. You may select 1-step (for i.i.d. innovations) to compute the Arellano-Bond 1step estimator, 2-step (update weights once), to compute the ArellanoBond 2-step estimator, or n-step (iterate to convergence), to iterate the weight calculations. In the first case, EViews will provide you with choices for computing the standard errors, but here only White period robust standard errors are allowed. Clicking on Next takes you to the final page. Click on Finish to return to the Equation Estimation dialog.

The standard errors that we report here are the standard Arellano-Bond 2-step estimator standard errors. Note that there is evidence in the literature that the standard errors for the two-step estimator may not be reliable. The bottom portion of the output displays additional information about the specification and summary statistics:

Note in particular the results labeled “J-statistic” and “Instrument rank”. Since the reported J-statistic is simply the Sargan statistic (value of the GMM objective function at estimated parameters), and the instrument rank of 38 is greater than the number of estimated coefficients (13), we may use it to construct the Sargan test of over-identifying restrictions. It is worth noting here that the J-statistic reported by a panel equation differs from that reported by an ordinary equation by a factor equal to the number of observations. Under the null hypothesis that the over-identifying restrictions are valid, the Sargan statistic is distributed as a x ( p – k ) , where k is the number of estimated coefficients and p is the instrument rank. The p-value of 0.22 in this example may be computed using “scalar pval = @chisq(30.11247, 25)”.

Panel Equation Testing
Omitted Variables Test
You may perform an F-test of the joint significance of variables that are presently omitted from a panel or pool equation estimated by list. Select View/Coefficient Diagnostics/Omitted Variables - Likelihood Ratio... and in the resulting dialog, enter the names of the variables you wish to add to the default specification. If estimating in a pool setting, you should enter the desired pool or ordinary series in the appropriate edit box (common, cross-section specific, period specific). When you click on OK, EViews will first estimate the unrestricted specification, then form the usual F-test, and will display both the test results as well as the results from the unrestricted specification in the equation or pool window. Adapting Example 10.6 from Wooldridge (2002, p. 282) slightly, we may first estimate a pooled sample equation for a model of the effect of job training grants on LSCRAP using first differencing. The restricted set of explanatory variables includes a constant and D89. The results from the restricted estimator are given by:

Here, the test statistics do not reject, at conventional significance levels, the null hypothesis that D(GRANT) and D(GRANT_1) are jointly irrelevant. The remainder of the results shows summary information and the test equation estimated under the unrestricted alternative:

Note that if appropriate, the alternative specification will be estimated using the cross-section or period GLS weights obtained from the restricted specification. If these weights were not saved with the restricted specification and are not available, you may first be asked to reestimate the original specification.

Redundant Variables Test
You may perform an F-test of the joint significance of variables that are presently included in a panel or pool equation estimated by list. Select View/Coefficient Diagnostics/Redundant Variables - Likelihood Ratio... and in the resulting dialog, enter the names of the variables in the current specification that you wish to remove in the restricted model. When you click on OK, EViews will estimate the restricted specification, form the usual Ftest, and will display the test results and restricted estimates. Note that if appropriate, the alternative specification will be estimated using the cross-section or period GLS weights obtained from the unrestricted specification. If these weights were not saved with the specification and are not available, you may first be asked to reestimate the original specification. To illustrate the redundant variables test, consider Example 10.4 from Wooldridge (2002, p. 262), where we test for the redundancy of GRANT and GRANT_1 in a specification estimated with cross-section random effects. The top portion of the unrestricted specification is given by:

The important thing to note is that the restricted specification removes the test variables GRANT and GRANT_1. Note further that the output indicates that we are using existing estimates of the random component variances (“Use pre-specified random component estimates”), and that the displayed results for the effects match those for the unrestricted specification.

Fixed Effects Testing
EViews provides built-in tools for testing the joint significance of the fixed effects estimates in least squares specifications. To test the significance of your effects you must first estimate the unrestricted specification that includes the effects of interest. Next, select View/Fixed/ Random Effects Testing/Redundant Fixed Effects – Likelihood Ratio. EViews will estimate the appropriate restricted specifications, and will display the test output as well as the results for the restricted specifications. Note that where the unrestricted specification is a two-way fixed effects estimator, EViews will test the joint significance of all of the effects as well as the joint significance of the cross-section effects and the period effects separately.

Note that the specification has both cross-section and period fixed effects. When you select the fixed effect test from the equation menu, EViews estimates three restricted specifications: one with period fixed effects only, one with cross-section fixed effects only, and one with only a common intercept. The test results are displayed at the top of the results window:

Notice that there are three sets of tests. The first set consists of two tests (“Cross-section F” and “Cross-section Chi-square”) that evaluate the joint significance of the cross-section effects using sums-of-squares (F-test) and the likelihood function (Chi-square test). The corresponding restricted specification is one in which there are period effects only. The two statistic values (113.35 and 682.64) and the associated p-values strongly reject the null that the cross-section effects are redundant. The next two tests evaluate the significance of the period dummies in the unrestricted model against a restricted specification in which there are cross-section effects only. Both forms of the statistic strongly reject the null of no period effects. The remaining results evaluate the joint significance of all of the effects, respectively. Both of the test statistics reject the restricted model in which there is only a single intercept. Below the test statistic results, EViews displays the results for the test equations. In this example, there are three distinct restricted equations so EViews shows three sets of estimates. Lastly, note that this test statistic is not currently available for instrumental variables and GMM specifications.

Hausman Test for Correlated Random Effects
A central assumption in random effects estimation is the assumption that the random effects are uncorrelated with the explanatory variables. One common method for testing this assumption is to employ a Hausman (1978) test to compare the fixed and random effects estimates of coefficients (for discussion see, for example Wooldridge (2002, p. 288), and Baltagi (2005, p. 66)). To perform the Hausman test, you must first estimate a model with your random effects specification. Next, select View/Fixed/Random Effects Testing/Correlated Random Effects - Hausman Test. EViews will automatically estimate the corresponding fixed effects specifications, compute the test statistics, and display the results and auxiliary equations.

Next we select the Hausman test from the equation menu by clicking on View/Fixed/Random Effects Testing/Correlated Random Effects - Hausman Test. EViews estimates the corresponding fixed effects estimator, evaluates the test, and displays the results in the equation window. If the original specification is a two-way random effects model, EViews will test the two sets of effects separately as well as jointly. There are three parts to the output. The top portion describes the test statistic and provides a summary of the results. Here we have:
Correlated Random Effects - Hausman Test Equation: Untitled Test cross-section random effects Chi-Sq. Statistic 2.131366

Test Summary Cross-section random

Chi-Sq. d.f. 2

Prob. 0.3445

The statistic provides little evidence against the null hypothesis that there is no misspecification.

676—Chapter 37. Panel Estimation

The next portion of output provides additional test detail, showing the coefficient estimates from both the random and fixed effects estimators, along with the variance of the difference and associated p-values for the hypothesis that there is no difference. Note that in some cases, the estimated variances can be negative so that the probabilities cannot be computed.
Cross-section random effects test comparisons: Variable F C01 Fi xed 0.110124 0.310065 Random 0.109781 0.308113 V ar(Diff.) 0.000031 0.000006 P rob. 0.9 506 0.4 332

In some cases, EViews will automatically drop non-varying variables in order to construct the test statistic. These dropped variables will be indicated in this latter estimation output.

Estimation Background
The basic class of models that can be estimated using panel techniques may be written as:

Y it = f ( X it, b ) + d i + g t + e it

(37.1)

Estimation Background—677

The leading case involves a linear conditional mean specification, so that we have:

Y it = a + X it ¢b + d i + g t + e it

(37.2)

where Y it is the dependent variable, and X it is a k -vector of regressors, and e it are the error terms for i = 1, 2, º, M cross-sectional units observed for dated periods t = 1, 2, º, T . The a parameter represents the overall constant in the model, while the d i and g t represent cross-section or period specific effects (random or fixed). Note that in contrast to the pool specifications described in Equation (35.2) on page 601, EViews panel equations allow you to specify equations in general form, allowing for nonlinear coefficients mean equations with additive effects. Panel equations do not automatically allow for b coefficients that vary across cross-sections or periods, but you may, of course, create interaction variables that permit such variation. Other than these differences, the pool equation discussion of “Estimation Background” on page 601 applies to the estimation of panel equations. In particular, the calculation of fixed and random effects, GLS weighting, AR estimation, and coefficient covariances for least squares and instrumental variables is equally applicable in the present setting. Accordingly, the remainder of this discussion will focus on a brief review of the relevant econometric concepts surrounding GMM estimation of panel equations.

GMM Details
The following is a brief review of GMM estimation and dynamic panel estimators. As always, the discussion is merely an overview. For detailed surveys of the literature, see Wooldridge (2002) and Baltagi (2005).

Background
The basic GMM panel estimators are based on moments of the form,
M M

g(b) =

i=1

Â

gi ( b ) =

i=1

Â Z i ¢ei ( b )

(37.3)

where Z i is a T i ¥ p matrix of instruments for cross-section i , and,

e i ( b ) = ( Y i – f ( X it, b ) )

(37.4)

In some cases we will work symmetrically with moments where the summation is taken over periods t instead of i . GMM estimation minimizes the quadratic form:

The basics of GMM estimation involve: (1) specifying the instruments Z , (2) choosing the weighting matrix H , and (3) determining an estimator for L . It is worth pointing out that the summations here are taken over individuals; we may equivalently write the expressions in terms of summations taken over periods. This symmetry will prove useful in describing some of the GMM specifications that EViews supports. A wide range of specifications may be viewed as specific cases in the GMM framework. For example, the simple 2SLS estimator, using ordinary estimates of the coefficient covariance, specifies:

so that we have a White cross-section robust coefficient covariance estimator. Additional robust covariance methods are described in detail in “Robust Coefficient Covariances” on page 611. In addition, EViews supports a variety of weighting matrix choices. All of the choices available for covariance calculation are also available for weight calculations in the standard panel GMM setting: 2SLS, White cross-section, White period, White diagonal, Cross-section SUR (3SLS), Cross-section weights, Period SUR, Period weights. An additional differenced error weighting matrix may be employed when estimating a dynamic panel data specification using GMM. The formulae for these weights are follow immediately from the choices given in “Robust Coefficient Covariances” on page 611. For example, the Cross-section SUR (3SLS) weighting matrix is computed as:

 –1 T  ˆ H =  T Â Z t ¢Q M Z t   t = 1

–1

(37.15)

ˆ where Q M is an estimator of the contemporaneous covariance matrix. Similarly, the White period weights are given by:

 –1 M  ˆˆ H =  M Â Z i ¢e i e i ¢Z i   i= 1

–1

(37.16)

These latter GMM weights are associated with specifications that have arbitrary serial correlation and time-varying variances in the disturbances.

680—Chapter 37. Panel Estimation

GLS Specifications
EViews allows you to estimate a GMM specification on GLS transformed data. Note that the moment conditions are modified to reflect the GLS weighting:

First-differencing this specification eliminates the individual effect and produces an equation of the form:

DY it =

j= 1

Â r j DY it – j + DX it ¢b + De it

p

(37.19)

which may be estimated using GMM techniques. Efficient GMM estimation of this equation will typically employ a different number of instruments for each period, with the period-specific instruments corresponding to the different numbers of lagged dependent and predetermined variables available at a given period. Thus, along with any strictly exogenous variables, one may use period-specific sets of instruments corresponding to lagged values of the dependent and other predetermined variables. Consider, for example, the motivation behind the use of the lagged values of the dependent variable as instruments in Equation (37.19). If the innovations in the original equation are i.i.d., then in t = 3 , the first period available for analysis of the specification, it is obvious that Y i1 is a valid instrument since it is correlated with DY i2 , but uncorrelated with De i3 . Similarly, in t = 4 , both Y i2 and Y i1 are potential instruments. Continuing in this vein, we may form a set of predetermined instruments for individual i using lags of the dependent variable:

Y i1 Wi = 0 º 0

0 Y i1 º 0

0 Y i2 º 0

º º º º

º º º Y i1

º º º Y i2

º º º º

0 0 º Y iT i – 2
(37.20)

Similar sets of instruments may be formed for each predetermined variables.

References—681

Assuming that the e it are not autocorrelated, the optimal GMM weighting matrix for the differenced specification is given by,

H
where Y is the matrix,

d

 –1 M  =  M Â Z i ¢YZ i   i= 1

–1

(37.21)

2 –1 1 Y = -- º 2 0 0

–1 2 º 0 0

0 0 º 0 0

º º º º º

0 0 º 2 –1

0 0 2 º j –1 2

(37.22)

and where Z i contains a mixture of strictly exogenous and predetermined instruments. Note that this weighting matrix is the one used in the one-step Arellano-Bond estimator. Given estimates of the residuals from the one-step estimator, we may replace the H weighting matrix with one estimated using computational forms familiar from White period covariance estimation:
d

 –1 M  H=  M Â Z i ¢ De i De i ¢Z i   i= 1

–1

(37.23)

This weighting matrix is the one used in the Arellano-Bond two-step estimator. Lastly, we note that an alternative method of transforming the original equation to eliminate the individual effect involves computing orthogonal deviations (Arellano and Bover, 1995). We will not reproduce the details on here but do note that residuals transformed using orthogonal deviations have the property that the optimal first-stage weighting matrix for the transformed specification is simply the 2SLS weighting matrix:

Chapter 38. Cointegration Testing
The finding that many macro time series may contain a unit root has spurred the development of the theory of non-stationary time series analysis. Engle and Granger (1987) pointed out that a linear combination of two or more non-stationary series may be stationary. If such a stationary linear combination exists, the non-stationary time series are said to be cointegrated. The stationary linear combination is called the cointegrating equation and may be interpreted as a long-run equilibrium relationship among the variables. This chapter describes several tools for testing for the presence of cointegrating relationships among non-stationary variables in non-panel and panel settings. The first two parts of this chapter focus on cointegration tests employing the Johansen (1991, 1995) system framework or Engle-Granger (1987) or Phillips-Ouliaris (1990) residual based test statistics. The final section describes cointegration tests in panel settings where you may compute the Pedroni (1999), Pedroni (2004), and Kao (1999) tests as well as a Fisher-type test using an underlying Johansen methodology (Maddala and Wu, 1999). The Johansen tests may be performed using a Group object or an estimated Var object. The residual tests may be computed using a Group object or an Equation object estimated using nonstationary regression methods. The panel tests may be conducted using a Pool object or a Group object in a panel workfile setting. Note that additional cointegration tests are offered as part of the diagnostics for an equation estimated using nonstationary methods. See “Testing for Cointegration” on page 234. If cointegration is detected, Vector Error Correction (VEC) or nonstationary regression methods may be used to estimate the cointegrating equation. See “Vector Error Correction (VEC) Models” on page 478 and Chapter 25. “Cointegrating Regression,” beginning on page 219 for details.

Johansen Cointegration Test
EViews supports VAR-based cointegration tests using the methodology developed in Johansen (1991, 1995) performed using a Group object or an estimated Var object. Consider a VAR of order p :

y t = A 1 y t – 1 + º + A p y t – p + Bx t + e t

(38.1)

where y t is a k -vector of non-stationary I(1) variables, x t is a d -vector of deterministic variables, and e t is a vector of innovations. We may rewrite this VAR as,

Dy t = Py t – 1 +

p–1

i= 1

Â G i Dy t – i + Bx t + e t

(38.2)

686—Chapter 38. Cointegration Testing

where:

P =

i=1

Â

p

A i – I,

Gi = –

j = i +1

Â

p

Aj

(38.3)

Granger’s representation theorem asserts that if the coefficient matrix P has reduced rank r < k , then there exist k ¥ r matrices a and b each with rank r such that P = ab¢ and b¢y t is I(0). r is the number of cointegrating relations (the cointegrating rank) and each column of b is the cointegrating vector. As explained below, the elements of a are known as the adjustment parameters in the VEC model. Johansen’s method is to estimate the P matrix from an unrestricted VAR and to test whether we can reject the restrictions implied by the reduced rank of P .

How to Perform a Johansen Cointegration Test
To carry out the Johansen cointegration test, select View/Cointegration Test/Johansen System Cointegration Test... from a group window or View/Cointegration Test... from a Var object window. The Cointegration Test Specification page prompts you for information about the test. The dialog will differ slightly depending on whether you are using a group or an estimated Var object to perform your test. We show here the group dialog; the Var dialog has an additional page as described in “Imposing Restrictions” on page 692. Note that since this is a test for cointegration, this test is only valid when you are working with series that are known to be nonstationary. You may wish first to apply unit root tests to each series in the VAR. See “Unit Root Testing” on page 379 for details on carrying out unit root tests in EViews.

Deterministic Trend Specification
Your series may have nonzero means and deterministic trends as well as stochastic trends. Similarly, the cointegrating equations may have intercepts and deterministic trends. The asymptotic distribution of the LR test statistic for cointegration does not have the usual 2 x distribution and depends on the assumptions made with respect to deterministic trends.

Johansen Cointegration Test—687

Therefore, in order to carry out the test, you need to make an assumption regarding the trend underlying your data. For each row case in the dialog, the COINTEQ column lists the deterministic variables that appear inside the cointegrating relations (error correction term), while the OUTSIDE column lists the deterministic variables that appear in the VEC equation outside the cointegrating relations. Cases 2 and 4 do not have the same set of deterministic terms in the two columns. For these two cases, some of the deterministic term is restricted to belong only in the cointegrating relation. For cases 3 and 5, the deterministic terms are common in the two columns and the decomposition of the deterministic effects inside and outside the cointegrating space is not uniquely identified; see the technical discussion below. In practice, cases 1 and 5 are rarely used. You should use case 1 only if you know that all series have zero mean. Case 5 may provide a good fit in-sample but will produce implausible forecasts out-of-sample. As a rough guide, use case 2 if none of the series appear to have a trend. For trending series, use case 3 if you believe all trends are stochastic; if you believe some of the series are trend stationary, use case 4. If you are not certain which trend assumption to use, you may choose the Summary of all 5 trend assumptions option (case 6) to help you determine the choice of the trend assumption. This option indicates the number of cointegrating relations under each of the 5 trend assumptions, and you will be able to assess the sensitivity of the results to the trend assumption. We may summarize the five deterministic trend cases considered by Johansen (1995, p. 80– 84) as: 1. The level data y t have no deterministic trends and the cointegrating equations do not have intercepts:

The terms associated with a ^ are the deterministic terms “outside” the cointegrating relations. When a deterministic term appears both inside and outside the cointegrating relation, the decomposition is not uniquely identified. Johansen (1995) identifies the part that belongs inside the error correction term by orthogonally projecting the exogenous terms onto the a space so that a ^ is the null space of a such that a¢a ^ = 0 . EViews uses a different identification method so that the error correction term has a sample mean of zero. More specifically, we identify the part inside the error correction term by regressing the cointegrating relations b¢y t on a constant (and linear trend).

Exogenous Variables
The test dialog allows you to specify additional exogenous variables x t to include in the test VAR. The constant and linear trend should not be listed in the edit box since they are specified using the five Trend Specification options. If you choose to include exogenous variables, be aware that the critical values reported by EViews do not account for these variables. The most commonly added deterministic terms are seasonal dummy variables. Note, however, that if you include standard 0–1 seasonal dummy variables in the test VAR, this will affect both the mean and the trend of the level series y t . To handle this problem, Johansen (1995, page 84) suggests using centered (orthogonalized) seasonal dummy variables, which shift the mean without contributing to the trend. Centered seasonal dummy variables for quarterly and monthly series can be generated by the commands:
series d_q = @seas(q) - 1/4 series d_m = @seas(m) - 1/12

for quarter q and month m , respectively.

Lag Intervals
You should specify the lags of the test VAR as pairs of intervals. Note that the lags are specified as lags of the first differenced terms used in the auxiliary regression, not in terms of the levels. For example, if you type “1 2” in the edit field, the test VAR regresses Dy t on Dyt –1 , Dyt – 2 , and any other exogenous variables that you have specified. Note that in terms of the level series y t the largest lag is 3. To run a cointegration test with one lag in the level series, type “0 0” in the edit field.

Critical Values
By default, EViews will compute the critical values for the test using MacKinnon-HaugMichelis (1999) p-values. You may elect instead to report the Osterwald-Lenum (1992) at the 5% and 1% levels by changing the radio button selection from MHM to OsterwaldLenum.

As indicated in the header of the output, the test assumes no trend in the series with a restricted intercept in the cointegration relation (We computed the test using assumption 2 in the dialog, Intercept (no trend) in CE - no intercept in VAR), includes three orthogonalized seasonal dummy variables D1–D3, and uses one lag in differences (two lags in levels) which is specified as “1 1” in the edit field.

Number of Cointegrating Relations
The next portion of the table reports results for testing the number of cointegrating relations. Two types of test statistics are reported. The first block reports the so-called trace statistics and the second block (not shown above) reports the maximum eigenvalue statistics. For each block, the first column is the number of cointegrating relations under the null hypothesis, the second column is the ordered eigenvalues of the P matrix in (38.3), the third column is the test statistic, and the last two columns are the 5% and 1% critical values. The (nonstandard distribution) critical values are taken from MacKinnon-Haug-Michelis (1999) so they differ slightly from those reported in Johansen and Juselius (1990).

To determine the number of cointegrating relations r conditional on the assumptions made about the trend, we can proceed sequentially from r = 0 to r = k – 1 until we fail to reject. The result of this sequential testing procedure is reported at the bottom of each block. The trace statistic reported in the first block tests the null hypothesis of r cointegrating relations against the alternative of k cointegrating relations, where k is the number of endogenous variables, for r = 0, 1, º, k – 1 . The alternative of k cointegrating relations corresponds to the case where none of the series has a unit root and a stationary VAR may be specified in terms of the levels of all of the series. The trace statistic for the null hypothesis of r cointegrating relations is computed as:

LR tr ( r k ) = – T

i=r + 1

Â

k

log ( 1 – l i )

(38.4)

where l i is the i-th largest eigenvalue of the P matrix in (38.3) which is reported in the second column of the output table. The second block of the output reports the maximum eigenvalue statistic which tests the null hypothesis of r cointegrating relations against the alternative of r + 1 cointegrating relations. This test statistic is computed as:

for r = 0, 1, º, k – 1 . There are a few other details to keep in mind: • Critical values are available for up to k = 10 series. Also note that the critical values depend on the trend assumptions and may not be appropriate for models that contain other deterministic regressors. For example, a shift dummy variable in the test VAR implies a broken linear trend in the level series y t . • The trace statistic and the maximum eigenvalue statistic may yield conflicting results. For such cases, we recommend that you examine the estimated cointegrating vector and base your choice on the interpretability of the cointegrating relations; see Johansen and Juselius (1990) for an example. • In some cases, the individual unit root tests will show that some of the series are integrated, but the cointegration test will indicate that the P matrix has full rank ( r = k ). This apparent contradiction may be the result of low power of the cointegration tests, stemming perhaps from a small sample size or serving as an indication of specification error.

Cointegrating Relations
The second part of the output provides estimates of the cointegrating relations b and the adjustment parameters a . As is well known, the cointegrating vector b is not identified unless we impose some arbitrary normalization. The first block reports estimates of b and a based on the normalization b¢S 11 b = I , where S 11 is defined in Johansen (1995). Note that the transpose of b is reported under Unrestricted Cointegrating Coefficients so that the first row is the first cointegrating vector, the second row is the second cointegrating vector, and so on.
Unrestricted Cointegrating Coefficients (n ormalized by b'*S11*b=I): LRM -21.97409 14.6559 8 7.94655 2 1.02449 3 LRY 22.69811 -20.0508 9 -25.6408 0 -1.92976 1 IBO -114.4173 3.561148 4.277513 24.99712 IDE 92.64010 100.2632 -44 .87727 -14 .64825 C 133.1615 -62.59345 62.74888 -2.318655

The remaining blocks report estimates from a different normalization for each possible number of cointegrating relations r = 0, 1, º, k – 1 . This alternative normalization expresses the first r variables as functions of the remaining k – r variables in the system.

692—Chapter 38. Cointegration Testing

Asymptotic standard errors are reported in parentheses for the parameters that are identified. In our example, for one cointegrating equation we have:
1 Cointegr ating Equati on(s): Log likelihood 669.1154

Imposing Restrictions
Since the cointegrating vector b is not fully identified, you may wish to impose your own identifying restrictions. If you are performing your Johansen cointegration test using an estimated Var object, EViews offers you the opportunity to impose restrictions on b . Restrictions can be imposed on the cointegrating vector (elements of the b matrix) and/or on the adjustment coefficients (elements of the a matrix) To perform the cointegration test from a Var object, you will first need to estimate a VAR with your variables as described in “Estimating a VAR in EViews” on page 460. Next, select View/Cointegration Test... from the Var menu and specify the options in the Cointegration Test Specification tab as explained above. Then bring up the VEC Restrictions tab. You will enter your restrictions in the edit box that appears when you check the Impose Restrictions box:

Johansen Cointegration Test—693

A full description of how to enter your restrictions is provided in “Imposing Restrictions” on page 481.

Results of Restricted Cointegration Test
If you impose restrictions in the Cointegration Test view, the top portion of the output will display the unrestricted test results as described above. The second part of the output begins by displaying the results of the LR test for binding restrictions.
Restrictions: a(3,1)=0

If the restrictions are not binding for a particular rank, the corresponding rows will be filled with NAs. If the restrictions are binding but the algorithm did not converge, the corresponding row will be filled with an asterisk “*”. (You should redo the test by increasing the number of iterations or relaxing the convergence criterion.) For the example output displayed above, we see that the single restriction a 31 = 0 is binding only under the assumption that

694—Chapter 38. Cointegration Testing

there is one cointegrating relation. Conditional on there being only one cointegrating relation, the LR test does not reject the imposed restriction at conventional levels. The output also reports the estimated b and a imposing the restrictions. Since the cointegration test does not specify the number of cointegrating relations, results for all ranks that are consistent with the specified restrictions will be displayed. For example, suppose the restriction is:
B(2,1) = 1

Since this is a restriction on the second cointegrating vector, EViews will display results for ranks r = 2, 3, º, k – 1 (if the VAR has only k = 2 variables, EViews will return an error message pointing out that the “implied rank from restrictions must be of reduced order”). For each rank, the output reports whether convergence was achieved and the number of iterations. The output also reports whether the restrictions identify all cointegrating parameters under the assumed rank. If the cointegrating vectors are identified, asymptotic standard errors will be reported together with the parameters b .

Single-Equation Cointegration Tests
You may use a group or an equation object estimated using cointreg to perform Engle and Granger (1987) or Phillips and Ouliaris (1990) single-equation residual-based cointegration tests. A description of the single-equation model underlying these tests is provided in “Background” on page 219. Details on the computation of the tests and the associated options may be found in “Residual-based Tests,” on page 234. Briefly, the Engle-Granger and Phillips-Ouliaris residual-based tests for cointegration are simply unit root tests applied to the residuals obtained from a static OLS cointegrating regression. Under the assumption that the series are not cointegrated, the residuals are unit root nonstationary. Therefore, a test of the null hypothesis of no cointegration against the alternative of cointegration may be constructed by computing a unit root test of the null of residual nonstationarity against the alternative of residual stationarity.

How to Perform a Residual-Based Cointegration Test
We illustrate the single-equation cointegration tests using Hamilton’s (1994) purchasing power parity example (p. 598) for the log of the U.S. price level (P_T), log of the Dollar-Lira exchange rate (S_T), and the log of the Italian price level (PSTAR_T) from 1973m1 to 1989m10. We will use these data, which are provided in “Hamilton_rates.WF1”, to construct Engle-Granger and Phillips-Ouliaris tests assuming the constant is the only deterministic regressor in the cointegrating equation. To carry out the Engle-Granger of Phillips-Ouliaris cointegration tests, first create a group, say G1, containing the series P_T, S_T, and PSTAR_T, then select View/Cointegration

Single-Equation Cointegration Tests—695

Test/Single-Equation Cointegration Test from the group toolbar or main menu. The Cointegration Test Specification page opens to prompt you for information about the test. The combo box at the top allows you to choose between the default EngleGranger test or the Phillips-Ouliaris test. Below the combo are the options for the test statistic. The Engle-Granger test requires a specification for the number of lagged differences to include in the test regression, and whether to d.f. adjust the standard error estimate when forming the ADF test statistics. To match Hamilton’s example, we specify a Fixed (Userspecified) lag specification of 12, and retain the default d.f. correction of the standard error estimate. The right-side of the dialog is used to specify the form of the cointegrating equation. The main cointegrating equation is described in the Equation specification section. You should use the Trend specification combo to choose from the list of pre-specified deterministic trend variable assumptions (None, Constant (Level), Linear Trend, Quadratic Trend). If you wish to include deterministic regressors that are not offered in the pre-specified list, you may enter the series names or expressions in the Deterministic regressors edit box. For our example, we will leave the settings at their default values, with the Trend specification set to Constant (Level), and no additional deterministic regressors specified. The Regressors specification section should be used to specify any deterministic trends or other regressors that should be included in the regressors equations but not in the cointegrating equation. In our example, Hamilton points to evidence of non-zero drift in the regressors, so we will select Linear trend in the Additional trends combo. Click on OK to compute and display the test results.

The top two portions of the output describe the test setup and summarize the test results. Regarding the test results, note that EViews computes both the Engle-Granger tau-statistic (t-statistic) and normalized autocorrelation coefficient (which we term the z-statistic) for residuals obtained using each series in the group as the dependent variable in a cointegrating regression. Here we see that the test results are broadly similar for different dependent variables, with the tau-statistic uniformly failing to reject the null of no cointegration at conventional levels. The results for the z-statistics are mixed, with the residuals from the P_T equation rejecting the unit root null at the 5% level. On balance, however, the test statistics suggest that we cannot reject the null hypothesis of no cointegration. The bottom portion of the results show intermediate calculations for the test corresponding to each dependent variable. “Residual-based Tests,” on page 234 offers a discussion of these statistics. We do note that there are only 2 stochastic trends in the asymptotic distribution (instead of the 3 corresponding to the number of variables in the group) as a result of our assumption of a non-zero drift in the regressors. Alternately, you may compute the Phillips-Ouliaris test statistic. Once again select View/ Cointegration Test/Single-Equation Cointegration Test from the Group toolbar or main menu, but this time choose Phillips-Ouliaris in the Test Method combo.

Single-Equation Cointegration Tests—697

The right-hand side of the dialog, which describes the cointegrating regression and regressors specifications, should be specified as before. The left-hand side of the dialog changes to show a single Options button for controlling the estimation of the Long-run variance used in the Phillips-Ouliaris test, and the checkbox for d.f Adjustment of the variance estimates. The default settings instruct EViews to compute these long-run variances using a non-prewhitened Bartlett kernel estimator with a fixed Newey-West bandwidth. We match the Hamilton example settings by turning off the d.f. adjustment and by clicking on the Options button and using the Bandwidth method combo to specify a User-specified bandwidth value of 13. Click on the OK button to accept the Options, then on OK again to compute the test statistics and display the results:

In contrast with the Engle-Granger tests, the results are quite similar for all six of the tests with the Phillips-Ouliaris test not rejecting the null hypothesis that the series are not cointegrated. As before, the bottom portion of the output displays intermediate results for the test associated with each dependent variable.

Panel Cointegration Testing
The extensive interest in and the availability of panel data has led to an emphasis on extending various statistical tests to panel data. Recent literature has focused on tests of cointegration in a panel setting. EViews will compute one of the following types of panel cointegration tests: Pedroni (1999), Pedroni (2004), Kao (1999) and a Fisher-type test using an underlying Johansen methodology (Maddala and Wu 1999).

Performing Panel Cointegration Tests in EViews
You may perform a cointegration test using either a Pool object or a Group in a panel workfile setting. We focus here on the panel setting; conducting a cointegration test using a Pool

Panel Cointegration Testing—699

involves only minor differences in specification (see “Performing Cointegration Tests,” beginning on page 582 for a discussion of testing in the pooled data setting). To perform the panel cointegration test using a Group object you should first make certain you are in a panel structured workfile (Chapter 36. “Working with Panel Data,” on page 615). If you have a panel workfile with a single cross-section in the sample, you may perform one of the standard single-equation cointegration tests using your subsample. Next, open an EViews group containing the series of interest, and select Views/Cointegration Test/Panel Cointegration Test… to display the cointegration dialog. The combo box at the top of the dialog box allow you to choose between three types of tests: Pedroni (EngleGranger based), Kao (EngleGranger based), Fisher (combined Johansen). As you select different test types, the remainder of the dialog will change to present you with different options. Here, we see the options associated with the Pedroni test. (Note, the Pedroni test will only be available for groups containing seven or fewer series.) The customizable options associated with Pedroni and Kao tests are very similar to the options found in panel unit root testing (“Panel Unit Root Test” on page 391). The Deterministic trend specification portion of the dialog specifies the exogenous regressors to be included in the second-stage regression. You should select Individual intercept if you wish to include individual fixed effects, Individual intercept and individual trend if you wish to include both individual fixed effects and trends, or No intercept or trend to include no regressors. The Kao test only allows for Individual intercept. The Lag length section is used to determine the number of lags to be included in the second stage regression. If you select Automatic selection, EViews will determine the optimum lag using the information criterion specified in the combo box (Akaike, Schwarz, HannanQuinn). In addition you may provide a Maximum lag to be used in automatic selection. An empty field will instruct EViews to calculate the maximum lag for each cross-section based on the number of observations. The default maximum lag length for cross-section i is computed as:

700—Chapter 38. Cointegration Testing

int ( min(( T i – k ) § 3, 12) ⋅ ( T i § 100 )

1§4

)

where T i is the length of the cross-section i . Alternatively, you may provide your own value by selecting User specified, and entering a value in the edit field. The Pedroni test employs both parametric and non-parametric kernel estimation of the long run variance. You may use the Variance calculation and Lag length sections to control the computation of the parametric variance estimators. The Spectral estimation portion of the dialog allows you to specify settings for the non-parametric estimation. You may select from a number of kernel types (Bartlett, Parzen, Quadratic spectral) and specify how the bandwidth is to be selected (Newey-West automatic, Newey-West fixed, User specified). The 2§9 Newey-West fixed bandwidth is given by 4 ( T i § 100 ) . The Kao test uses the Lag length and the Spectral estimation portion of the dialog settings as described below. Here, we see the options for the Fisher test selection. These options are similar to the options available in the Johansen cointegration test (“Johansen Cointegration Test,” beginning on page 685). The Deterministic trend specification section determines the type of exogenous trend to be used. The Lag intervals section specifies the lag-pair to be used in estimation.

Panel Cointegration Details
Here, we provide a brief description of the cointegration tests supported by EViews. The Pedroni and Kao tests are based on Engle-Granger (1987) two-step (residual-based) cointegration tests. The Fisher test is a combined Johansen test.

Pedroni (Engle-Granger based) Cointegration Tests
The Engle-Granger (1987) cointegration test is based on an examination of the residuals of a spurious regression performed using I(1) variables. If the variables are cointegrated then the residuals should be I(0). On the other hand if the variables are not cointegrated then the residuals will be I(1). Pedroni (1999, 2004) and Kao (1999) extend the Engle-Granger framework to tests involving panel data.

Panel Cointegration Testing—701

Pedroni proposes several tests for cointegration that allow for heterogeneous intercepts and trend coefficients across cross-sections. Consider the following regression

for t = 1, º, T ; i = 1, º, N ; m = 1, º, M ; where y and x are assumed to be integrated of order one, e.g. I(1). The parameters a i and d i are individual and trend effects which may be set to zero if desired. Under the null hypothesis of no cointegration, the residuals e i, t will be I(1). The general approach is to obtain residuals from Equation (38.6) and then to test whether residuals are I(1) by running the auxiliary regression,

e it = r i e it – 1 + u it
or
pi

(38.7)

e it = r i e it – 1 +

j=1

Â w ij De it – j + v it

(38.8)

for each cross-section. Pedroni describes various methods of constructing statistics for testing for null hypothesis of no cointegration ( r i = 1 ). There are two alternative hypotheses: the homogenous alternative, ( r i = r ) < 1 for all i (which Pedroni terms the within-dimension test or panel statistics test), and the heterogeneous alternative, r i < 1 for all i (also referred to as the between-dimension or group statistics test). The Pedroni panel cointegration statistic ¿ N, T is constructed from the residuals from either Equation (38.7) or Equation (38.8). A total of eleven statistics with varying degree of properties (size and power for different N and T ) are generated. Pedroni shows that the standardized statistic is asymptotically normally distributed,

Kao (Engle-Granger based) Cointegration Tests
The Kao test follows the same basic approach as the Pedroni tests, but specifies cross-section specific intercepts and homogeneous coefficients on the first-stage regressors. In the bivariate case described in Kao (1999), we have

y it = a i + bx it + e it
for

(38.10)

702—Chapter 38. Cointegration Testing

y it = y it – 1 + u i, t x it = x it – 1 + e i, t

(38.11) (38.12)

for t = 1, º, T ; i = 1, º, N . More generally, we may consider running the first stage regression Equation (38.6), requiring the a i to be heterogeneous, b i to be homogeneous across cross-sections, and setting all of the trend coefficients g i to zero. Kao then runs either the pooled auxiliary regression,

e it = re it – 1 + v it
or the augmented version of the pooled specification,
p

(38.13)

˜ e it = r e it – 1 +

j=1

Â w j De it – j + v it

(38.14)

Under the null of no cointegration, Kao shows that following the statistics,

and the long run covariance is estimated using the usual kernel estimator

ˆ Q =

ˆ2 ˆ j 0u j 0ue ˆ ˆ2 j 0u e j 0e
(38.22)
T

1 = --N

i= 1

Â

N

1 --T

t =1

ˆ ˆ Â w it w it ¢ + --- Â T

1

•

k(t § b)

t = 1

t = t+1

ˆ ˆ ˆ ˆ Â ( w it w it – t ¢ + wit – t w it ¢ )

T

where k is one of the supported kernel functions and b is the bandwidth.

Combined Individual Tests (Fisher/Johansen)
Fisher (1932) derives a combined test that uses the results of the individual independent tests. Maddala and Wu (1999) use Fisher’s result to propose an alternative approach to testing for cointegration in panel data by combining tests from individual cross-sections to obtain at test statistic for the full panel. If p i is the p-value from an individual cointegration test for cross-section i , then under the null hypothesis for the panel,